Hi Z,
If both bits are ally, then the rivet you want will have to be ally also - or at least soft, so it won't burst the metal around the hole when you form it. The diameter of the rivet needs to be a close fit to the size of the hole (the tighter the better really) and it needs to be long enough to form a good tail - if you can get a handfull of commercial rivets with a round or domed head, allow about one and a half diameters worth of length to form the tail (ie if rivet is 4mm dia, allow 6mm for the tail). It is not absolutely necessary to have a dolly to fit the rivet head, just something solid for it to rest on. You can form the tail by tapping the tail, end on to swell the shank in the hole (making it watertight) and then forming a "blob" equal to about 60% of the original diameter (so the 6mm tail is now only 3mm tall). There are many more things to know about rivetting but one thing to be aware of with ally rivets is that they "work harden" if they're hit too many times - so don't take forever to form the tail or it will crack and drop out! Do some practice runs on any old piece of metal to get an idea before you start on your mess tins.
Pop rivets have given rivets in general a bad name as there are blind rivets that are as strong as nuts and bolts - speaking of which, it is probably easier to buy some small stainless nuts & bolts, tighten them into place, cut off any excess length and then hammer the end so the nuts wont come off and are nice and smooth so they wont catch your finger or harbour food waste.
ATB
Ogri the trog - Ex aircraft engineer, dealt with many thousands of different rivets.