Brass ax with a steel bit were cast in place more often than not, today we can silver solder or braze steel in place, properly fit of course. I typically use an old piece of file steel, forged to rough shape, dovetails filed and fit to the brass, easier to fit the brass to steel in a cold state. I will allow the joint to solidify by either method, then work my heat to the edge to hardening temp., quench the edge only hold for a few seconds withdraw the head and allow the tempering of the edge then quench the whole thing. Mind you, there is no intent of actually using but a fun practice and does give some integrity to the edge. We all know someone will inevitably want to test it out, nothing more embarrassing than to have an edge rollover or ding at the slightest bump. Go for it, a good way to learn some fun and rewarding skills. Just one school of thought on the subject anyway.
Mark