Does the Center of Mass perk only work with Guns, or will it work with other weapon types such as Explosives, Energy etc.?

I would guess regular guns and energy guns would work. with melee and explosives, you can't target specific spots, just the entire person. So I wouldn't think they would be effected by this perk. But with any type of laser or plasma guns, you should be able to target the torso. This is just a hunch of mine, I haven't confirmed it.

Any weapon that lets you specify the torso in VATS should work. However, its still not a good perk. Your better off taking something like sniper to make headshots in VATS more likely.