If you go with bolts, be sure the unthreaded portion of the bolt goes through both pieces. You will have to use a longer then normal bolt, then cut off excess threads. Also be sure the bolt fits the hole tight, normally the hole is drilled to fit the bolt. You want the bolt to fill the hole, just like the rivet does. Be ready for a fight if you go down this path, even with the heads ground off, you will still have to fight the rivet to get it out.
There was a thread just recently about tightening up loose rivets. It was said to heat the rivet head till red, the set it with the proper tools.