(The following comments are my personal opinions about "cute-em-ups" in general, aimed at no one in particular, with expletives added for emphasis and humor)
I absolutely hate the term "cute-em-up." 

Excuse my language, but classifying every shooter animated with cartoons rather than Giger-esque alien monsters as a "cute-em up" is f*cking retarded.
1)  For a game to be a cute-em up, even if the it is somewhat tongue-in-cheek or intended for older gamers, the content and humor must be strictly preteen--No dirty-old-man anime scenes or Air Zonk cow boobies.
2)  It cannot rock.  The music must be as weeny as the graphics.
Air Zonk is not a cute-em-up.  It was clearly marketed at a cynical teenage crowd and the music rocks (hence the sunglasses).  If anything, Zonk is more baddass than Bonk.  Hudson didn't set out to create some toned-down "baby Bonk" shooter in a cute magical dreamland.  I'm sorry the sprites happen to look like cartoons.
Cotton uses practically the same, if not the same, engine as Lords of Thunder; furthermore, zombies rip off their heads and throw them at you.  No f*cking way.  As for the cinema scenes, they're the same worthless anime crap that can be found in every other PCE game, regardless of genre.  Not a cute-em-up.
Ordyne, Fantasy Zone and L-Dis are cute-em-ups, I haven't played many of the others.