I adapt to things pretty well, like controllers and stuff (I don't know how and why people keep complaining about certain ones), but shooters (as in FPSes) and other 3D games like 3D platformers on handhelds might take a little longer for me to get used too. I haven't played the GBA FPSes currently out there.
See, when I hold a handheld, I'm mostly looking down at it. In an FPS or 3D game when you move forward, it'd be like moving downward...every time you move it looks like you're falling. This is not an issue on a vertical screen like a TV screen or monitor, but I'm not going to be holding the handheld straight in front of me to get the proper perspective. If handheld screens weren't so small, the surroundings wouldn't cause this relative downwardness.
But I haven't seen anyone else ever mention this as a problem, and I'd probably adapt eventually anyway, so maybe it's not a concern.
Seeing as how there are FPSes and other variations of shooters on the GBA already, a shooter on a DS could work, assuming the same, similar, or not too radical difference in control scheme.