When making such a thing, make the holes of the straps, and especially the roves, slightly subcaliber, so you can drive them home over the rivet with something like a small deep well socket. Cut the rivets off slightly proud with nippers (as close as you can get with the nippers is generally proud enough), then backing it up on an anvil or what have you peen the head well over, working all the way 'round with a ball peen hammer. The very talented can make kind of a pointed, four-sided pyramid rivet head this way, which is quite decorative; I'm quite happy with a dome-shaped round one which holds tight.
If you've measured correctly, you'll have to rivet the head together on the finished shaft. Once done, the shaft will break before the head comes off.
Lochaber axes generally had a sharpened haft, often shod with a steel or iron cone or point, which sadly is beyond my skill to produce. Besides, mine will be displayed upright in a flagpole base in front of a clan tent (and occasionally trooped with the parade of tartans) at the Games, so the square end works for me.