if you are careful or if the appearance afterwards doesn't matter then an angle grinder/ or smaller rotary tool(Dremel) with a cut-off wheel is also an option.The only problem with any of approaches is when the rivet starts to turn in the hole (usually occurs with trying to drill out a rivet)!
the last sentence in step four makes It sounds like the size doesn't really matter that much, you should mention that if it is too small you won't get your rivet through in the first place.G.
looks really great! so going to do something similar on boxes! Thank you!
Roger please READ what is written in step one and then remove your comments!