I've installed nose caps only with epoxy.
I've installed nose caps only with rivets.
I've installed nose caps with both epoxy and rivets. My preference.
I think to ease application of the rivets a little epoxy between the wood and the cap will stabilize the cap before you install the rivets. Allow the epoxy to set up well with the barrel in place, then remove the barrel and clean up any squeeze out. If you were frugal there will be very little or none. A little movement of the cap while installing the rivets can cause positioning problems. Keeping epoxy to minimum will not show and after you have the rivet/rivets installed, who can tell, it ain't coming off. If you're worrying about "historical correctness" I think it's much less of a crime than cast steel locks or worse glass bedding barrels, and those don't seem to bother anyone. Not denigrating any of these things, this is the 21 century.
There are a lot of ways to build these things, you have to find what works best for you. This works for me.