To do it right, that’s the way.I'd drill the wedge out, knock the haft out, clean the head up, dry the haft as you are but watch for warping or excessive cracking, refit the head properly, sand and blo the haft, sharpen the head.
Well actually I'd do none of that as I'd not find the time, but I'd like to do that.
I’d like to just get the head set right, de-rust, and hit with BLO.