I don't know anything about using a morse taper reamer in titanium, but if you are working with CP2 titanium, count yourself lucky. Maybe you know already, but it cuts well, even with HSS tooling. Just go slow speed and relatively heavy feed. Alloyed grades wouldn't be as forgiving.
I don't think you'll have too much trouble making it. I wouldn't expect the smoothest finish, especially once the tool starts wearing down.