Could you please provide a close-up of the inside of the hilt (hole for the tang)? That's a rare opportunity to have a closer look...
I'd also favor a traditional wood glue. However you'll need extra efforts to prepare a mold/cushion so that you can apply even pressure while the glue sets (a good bonds depends on the pressure but, obviously, you don't want to crush the hilt either); allow for some generous extra time (days) for the glue to set perfectly.
If this seems too much of a hassle, an good epoxy glue will also give an acceptable bond.
The break looks clean enough. Woods with higher amount of natural oils can result in weaker bonds though; you could try to degrease the break surface with acetone.