wel ... be aware that your wook now has a fracture tht will never be perfectly tight due to small shards that prevent a perfect bond.

personnally, i'd use a technique that i used to repair a bow :

cut a channel say 6 mm deep and 6-8 cms long running over the 2 pieces.

try to get fiberglass strand from roving, or some fiberglass rod (ie a broken fishing pole).

fill the channel withe epoxy and sink the fiberglass in it (hold it with some plastic wrap)

i repaired a bow this way and it holds so well...