@lyse I can suggest you a trick to do a "cold" welding.

Using a copper wire or a similarly malleable material, pass it through a drilled hole, hammer it on one end until flat, then do the same on the other side.

It does the same job of a rivet but it's flatter and look nicer on both sides, it's of course weaker but still strong enough for small objects.

It's sometimes used to reduce risk of deformities due to heat in hand-crafted jewelry and to reduce costs of small tools.

Thanks, @alexonit! Yeah, this classic rivet is a good, yet laborous alternative. I don't mind the work, I just don't have any copper at hand. I might give this some more thought, though.

@lyse I think you should be able to find some even in general stores in the hardware section.