Well you'd only be taking down 1/16" and a with good hand plane that's only a 10 minute job at most but I don't know what that would do to the integrity of the back of the bow.
A sander would do it quickly as well, but again, once you cut into the back it's the danger zone.
I guess if it's edge ringed you may be OK though.
Another thought is cutting the entire back off with a band saw and just replacing it.
Someone else here may have some good ideas.
CJ