All console ports of light gun games can be played with a controller, pretty much. It's the worst way to play these games because it's just not fast or precise enough, so you might find yourself setting it to easy or having to do a lot of memorization. I use to do it anyway with Virtua Cop cause I didn't have the light gun and still had fun, but I was a kid.
MAME and other arcade emulators let Model 2 Emulator (for House of the Dead) let you play using the mouse instead. It's definitely easier that way, and a bit more fun, though of course nothing beats a light gun.