I'd personally wait until spring, but because of where you live , you may be okay. I worry about hard winters damaging my trees in dormancy, but South Cackalacky has a milder season. If you do it, do it now and not in the middle of winter. Otherwise, spring is always good.
If it were my tree, I'd cut the right branch completely, and leave the other one to grow for a while. Plant it in the ground or larger container to thicken it out some more.