white wax wood
Cold Steel used to sell white wax wood crook handle canes, I still have one and it's among my favorites. They haven't offered them for several years now, and I don't know any other company which sells one. Several places (Bud K, etc) sell wax wood staffs or drill swords for MA training, but I haven't seen any canes for a while now.
Beech and birch are used for some less expensive gunstocks, if it's close grained enough for that, it ought to do OK for a cane. I generally use oak or hickory stock canes from farm supply wholesalers for making up canes for folks, they're widely available, tough and inexpensive. A little more weight to the wood is not a bad thing, I think.
lpl