Tightbond III Ultimate Wood Glue (green label). Should hold for decades.
In the past I've also used Original Tightbond Wood Glue (red label) and after 3 years of regular use on the razors its still holding like a champ.
I keep the wedge perimeter a little oversized, glue to one scale and let dry overnight. Then glue to the second scale. Then sand the wedge down so it's flush with the scales.
For clamping I use black paper
binder clips. If the nose surface is too rounded and slippery for the clips to stay on, I pull out one of the standard 12" bar clamps I keep around for home repair projects.