When I think of those Marble Knight Shantae palettes and how the half-genie herself was assigned not to the front-and-center lady on the title art, but rather the spear-wielding elf, I'm reminded of the speculation of which kinds of characters the Shantae cast would pick for D&D. Except we never mentioned which races they would select. So with that in mind, would elves really be the closest analogues to (half)-genies in a universe that generally doesn't have them?
I wrote a post or two about this ages ago.
In D&D the offspring of humans and genies (well, a few generations down the line) are Genasi.
So Shantae would be a Genasi Sorcerer most likely, with some folks recommending Druid. I'm partial to making a homebrew Kit/Build/Path for the Bard class.
Sky is a Human Ranger and Bolo is a Human Fighter.
Rottytops is a bit harder to stat out pre-3.X. In 3.5 there was the Necropolitan race from Libris Mortis. For 4E and 5E there's the Revenant race.
I'd go with Rottytops being a Revenant Rogue.
Risky Boots... Technically she's human right? Although she's been exposed to so much dark magic that one could make a case for some races that don't immediately come to mind (4E Shadar-Kai maybe?).
Class wise? Fighter for most editions, I suppose you could argue for Ranger. For 4E I'd use Warlord.
I'd use Goblin or Kobold stats as a starting point for the Tinkerbats.