A successful glue joint starts out with both sides clean, which we'll presume both sides of your split are.
Remove any pieces of errant grain that were displaced by the trauma. The goal of this is to remove any barrier to a literal hairline crack remaining when testing its reassembly, and out-of-place slivers of wood will hinder this big-time.
I think the choice of glue would be yours, from whatever formulas are recommended for wood by the various manufacturers. I'd go for either a waterproof wood glue or cyano acrylate gel, which gives sufficient working time.
Gluing without clamping is a waste of time, so make yourself a setup that will squeeze everything together straight and true, as you want it. You want to see glue pushed from the hairline crack. Clean off the excess that's squished out so you can keep track of the crack, and whatever you can reach when the clamping is finished. The solvent dampening the rag/toothbrush should be whatever the glue's maker recommends.
When revealed by un-clamping, cured glue that's where you don't want it may need to be removed mechanically--scraping/sanding.
Refinish the grip, or at least blend in the area of the repair, if needed.
That should do it.
Posting pics of your progress would be great...