Peening a rivit over when talking about a fragile 75 year old thin wooden camera is probably not a good idea ;-) Although you could of course do it with the right tools and care. I think I'd pass though and stick with the machine screws.
As to the mention above, I would beat that a #2 screw is stonger than that old split rivet! And my camera has 4 screws per side. Plenty strong enough for the handle.
As for those split rivits. Anyone know an on-line source for them???