You can't waveshine infinite Giga at all. Anyone with AR can try this. Get Fox vs Giga, then have Fox make frame-perfect waveshines against Giga. Now, have Giga put up his shield. Not only can he shield, but he can now also roll by buffering it with the C-stick.
In fact, try it with JC shines, and you'll find that Giga can still shield and roll out of it in the same way. For visual proof of this if you don't have AR, watch SDM's No Damage advanture clear with Fox. You see Giga roll out of frame perfect JC shines several times.
I think Giga would be an absolutely broken character. He dosn't even move when hit at low percents, even with strong attacks, which allows him to beat on any other character without them beeing able to do anything to him until he's at at least 50-70%. You'd think that would make him easy to combo, but it's not that theres no knockback, it's also that theres barely any stun.
Second, has anyone seen the priority on his upB? It outprioritizes anything, quite literally, even things comming from above (I don't think theres a single dair in the game that can get through it). It comes out in 4 frames, beeing the fourth fastest move in the game (after the shine, rest, and Ganon's jab at 1, 1 and 3 frames respectivly), he can use it out of shield, plus it combos into itself.
You know what? It's not just his upB, now that I think about it. It's any of his moves that outprioritize everything. There's simply no way to approach, juggle, combo or edgeguard him. And for crying out loud, he outranges Marth 2-fold with his grab...
And finally, the biggest reason he'd be broken: He can't be grabbed. To a lot of characters, they can't win ever just because of that. Try playing as Marth or CF without ever grabbing. Tough, isn't it?
EDIT: Forgot to mention he can chainthrow any other character in the game with his dthrow.