Of course, EVERYONE knows Hawken was building very few guns during the actual "mountain man era", whatever that was. And in all likelyhood none of them could afford the half stock rifle or the extremely expensive newfangled caplock innovation. Cargo lists from the era indicated a vast and overwhelming majority of all guns shipped west to the Rendezvous were smoothbore flintlocks.
In all the first person accounts I have read about the Fur Trade Era I have yet to come across any white trapper using a bow or mentioning shooting a bow. Doesn't mean it didn't happen. Even the Native Americans that came out west from the northeastern tribes were carrying guns.
Sounds like you are trying to be as historically accurate as possible within the constraints of our modern interpretations of 'rendezvous'. Fair enough! So here's a list of questions to consider:
1) What part of the Rockies (or prairies for that matter) that your personna was active?
2) What tribe(s) occupied that area?
3) Where did your personna spend the summers when the pelts were poor?
4) And what tribe(s) occupied that area?
Once you have that narrowed down you should have about a half dozen tribes to chose from. Find yourself a copy of Encyclopedia of Native American Bows, Arrows, & Quivers, Vol. 2, Plains & Southwest by Steve Allely and Jim Hamm.
If you can't find a bow in there that gets your heart racing you need to leave this Forum and never return! Things are now about to get difficult because you are probably more like me and you will want at least one of every design in there.