Here's what the aircraft assemblers do - rivet for living.

Grind off the head, gently, don't overheat the adjacent material. DO NOT torch as some may suggest (with all do respect, since I've received far more knowledge than I can contribute). Rivets by design are SOFT. That's how they expand in the hole when bucked, so torching to anneal is unneccessary and what you'll actual do is anneal the adjacent material, which is a bad thing. You don't want soft material holding a structural rivet.

Punch through the cylindrica remains. If neccessary, drill a small hole through the center - easy enough given the temper of the material (SOFT).

This will leave a clean hole ready for the new rivet, or whatever, and with the adjacent material still at the original temper.