I think they would have a Splatter Shot, since it's the poster-child weapon for splatoon. The Standard attacks I think would be mostly kicks and gun-buts with the Splatter Shot, though I do like the idea I saw to bring in other weapons here as well, like the Roller being wielded for Smash Attacks. Good thought I thought about standard attacks being like Mega Man, like
@OmegaDivider did, and having an ink-shot, but somehow it doesn't feel right to take that gimmick from him. Maybe if it was short ranged for the "jab", like Robin's chain attack with the wind tome. I do have a few more specific ideas for he specials though.
Standard B I initially pictured as being the Ink shots, like Fox's blaster and actually with a similar idea of leaving ink spots around. That said I like the Splat Bomb idea too.
Up B seems like there is one pretty obvious choice, the Super Jump! They rocket up with a decent amount of angle control, but not as good as Pit or Dark Pit's Power of Flight.
Side B, if the Splat Bomb wasn't taken by standard could be here, or it could be the Splat Charger, a ranged shot that you are committed to firing once you pull it. It charges for more range just like in the game. I could also see the Splash Wall here as some sort of slowing barrier, if the Splat Charger was used for a Mega Man like Side-Smash.
Now, Down B I had a concept for but I am not entirely sure how it should go. Essentially, I want the Inkling to leave Ink on the ground from other attacks, up to a cap, and the Down B is turning into squid form to use some sort of charging dash attack that works more fluidly if used on or near Ink. I imagine it having a straight down dive effect in the air and a small splat where they land, like Yoshi Bomb, or Bowser Bomb. However, if they dive into their own Ink, instead of having a long delay on landing, the Inkling jumps back out, spinning back into human form, while the spin flings a damaging splatter of Ink in a small circle around them, covering the move from being immediately countered on landing.
I really want them to have a reason to control ground with Ink, just like in Splatoon, which is where the Down B idea came from.