Aside from the other obvious game modes that would be fun sans power weapons, I think the perfect mode would be Elimination. Countless times I would be going along, trying to be sneaky and strategic, when suddenly, some crazy shotgun lover bursts out of nowhere shooting me in the face, and thus causing me to wait in purgatory for the round to end. It isn't so much the wait factor that would make Elimination-No Power Weapons a great Lab, but the fact that the playing field is more level for all players would make this mode fun. (Or you could just have Elimination-RPG's Only if that's what you want...)
I hope Naughty Dog considers this for a future Lab (that is if a Naughty Dog employee reads this).