I'm sure that playing Smash TV with 2 different joysticks will certainly work, however, as you point out, it will certainly feel different.
Smash TV is the whole reason I got into this hobby at all, so I decided to get 4 T-Stick Plus joysticks so they all feel the same. I also sprung for the optional ball top shafts so it's even more like a real Smash TV machine.