Maybe the cards work more like the command blocks from the Mario & Luigi games. You know (or maybe you don't, I dunno), where you select a block (or card, in this case) from a menu of a bunch of cards (or maybe hands, with an Attack hand containing the usual Jump/Hammer commands as cards as well as various other, maybe-one-time-use cards, while an Item hand would have all the items you've collected as cards, maybe a Run Away card...), then select a paint to apply to the card...
Or just play the card without painting it. It'd be used as a "standard" option, not having the advantages of a painted command, but also not using up any paint. Painting a card would, of course, use up your precious paint resources, but would grant additional effects to the card, creating a system where you need to decide whether that extra benefit now is worth using, since you may require a paint effect later before you've had a chance to get more paint (and of course there would be ways to replenish your paint outside of battle, though I wouldn't make them infinite, and ways to do so in battle, which would be rare or expensive consumable items; maybe it'd slooooooowly regen on its own too, so you wouldn't be absolutely screwed if you ran out at a bad time). While the different paint colors would have different effects, what exactly those effects would be would probably depend on which color was used an which card it was used on. For example, the Jump card could have just the normal jumps-on-the-enemy-twice that is standard for Mario RPGs, while painting Jump red could add more damage, while blue could allow Mario to jump on enemies he normally couldn't (like spiky enemies, or flaming ones), and yellow would allow Mario to jump on all enemies in a row (action command here would just make the jumps deal more damage, rather than allowing you to jump to the next enemy). How much paint was spent painting the card could affect the buff given by painting; for example, with the Jump card, spending a little yellow paint would make Mario jump once on each enemy, but using more yellow would make Mario jump on each enemy multiple times (more yellow spent adds more hits to each enemy). Additionally, you could combine paint colors to get multiple sets of properties at once, albeit at a reduced amount (to justify this in-game: since you're mixing the paints, it dilutes the benefits each color provides, or something); so sticking with the Jump card example, using some red and yellow paint would make Mario jump on each enemy, but with slightly increased damage.
Using this system, the Paint Hammer could also be rather interesting, I think. You could still paint the Hammer card (and a non-painted Hammer would just perform the Paper-Mario-standard pull-back-and-swing hammer attack), but painting wouldn't bestow new properties onto the attack. Instead, the Paint Hammer would be used to paint enemies, which could be the equivalent of inflicting status effects. Red paint could increase the damage enemies take from Mario's attacks, blue paint could remove enemy defenses (such as dulling spikes or putting out fires so that Mario can jump on the enemies), and yellow paint could make enemies deal less damage with their attacks. Using more paint would increase the duration of these effects, but additionally, if enough paint is used on the Hammer card for a single action (cumulative, so each color used contributes toward the threshold), the hammer will create a Color Splash, a paintsplosion that damages applies the status effects to all grounded enemies (and if you use a lot of paint, you could hit airborne foes with the Color Splash as well, though the amount of paint used would make it impractical).
Items would also be paintable, of course, and painting different items could have a variety of different effects, depending on the item used.
The run-away card I mentioned up in the first paragraph would not be paintable. You'd just play it and exit the fight, sans whatever penalty you lose for fleeing.
And Mario could spend a turn to paint himself, as well. Doing this would confer buffs onto him for as long as the paint remained, these buffs being roughly the opposite of the Paint Hammer debuffs for red and yellow, while blue could maybe give Mario more actions per turn. Paint would come closer to coming off of Mario for each action he takes. This is done primarily to balance blue paint (could become kinda broken otherwise, I fear).
Of course, cerain enemies would be able to take advantage of this as well (I'm picturing something like the Spiky Goomba from TTYD, but with a brush-hat instead of a spike-hat). These enemies would be able to paint not only themselves (some might not be able to paint themselves at all, for example the brush-head-goomba I mentioned above), but also their fellow enemies, giving them buffs while also undoing any paint-based debuffs you'd applied.
As for the reward you'd receive for completing fights... Well, you'd get Star Points (or some art-themed equivalent). When you gained a level (by getting 100, of course), you could power up your HP, increase the amount of one color of paint that you can hold (or maybe increase all three at once, though with a lesser increase if this is the case), or increase the maximum number of "Item" cards you could hold. The idea here is to make players choose between Mario being able to take more hits, being able to have more special cards, or being able to us more paint effects, on each level up. And of course, you wouldn't be able to make the same choice twice in a row, like in Paper Mario 64 and TTYD.
And just to indulge my fantasy of parters returning, let's say that some of the item cards you could collect would create paint versions of Mario's PM64 and TTYD partners, as well as Luigi, Peach, and Bowser, to perform various actions that they'd do. For example, you could have whatever enemy-scan thing is in this game (which would hopefully be a card you don't lose on use) would paint up Goombario or Goombella or Tippi (which one you get is random, and doesn't actually change anything, it's just a visual) to tell you about the enemy you're scanning, while a paint Peach would confer various benefits onto Mario, and paint Bow or Vivian (maybe random-selected, maybe separate cards with the same effect) could hide Mario, shielding him from all attacks and effects for one turn. These cards would probably be rarer than others, or really expensive if found in shops, but quite powerful. Additionally, painting these cards wouldn't power them up at all; instead, you'd have to spend a certain amount of paint (and possibly also certain colors; for example, a Luigi card would require blue and yellow (because green), while a Vivian would require red and blue (because purple)). The idea here is to balance the power of these cards by making them require the use of paint that you maybe would prefer using on something else. The Goombario/Goombella/Tippi card I mentioned above would be the exception; you wouldn't be able to paint it at all, since it's just an enemy-scan.
And of course, the fan from the reveal trailer would be in this subset of cards.
Oh, and since we're painting everything, I'd like to see a 4-squid Inkling team as a summonable thing from one of the item cards I just made up in the last paragraph.
Or maybe have an Inkling in the Hero Suit as a hidden extra boss.
Or at least have a Splatoon thing cameo somewhere. It'd just make sense, since both games rely quite a lot on painting (well, Splatoon's inking, but it's close enough).
