I took a hunting trip right after 9/11and did the UPS thing with my bow and arrow case. Got there as scheduled and there wasn't any damage. The airlines didn't have a surcharge then; I just didn't care to go through all the security hassle. I did it againon a spring hunt but had issues with the shotgun shell going through UPS. I endedhaving my buddy buy me a new boxbefore I arrived at camp and issue was solved.
Sending it through UPS or Fed Ex to ship your bow/gun/arrows is the way to go