Update:

Being cautious about it, I took the bow to my local bow shop yesterday. The two bow techs there said it wouldn't be a problem with one cut strand. They unserved my peep, pulled the cut strand back to the nock serving on one side and to the cam serving on the other, and cut off the loose ends. Their point was that a 2 color string has 4 ends under the servings, so now my 1 color string does too.

I made a few phone calls to other bow techs around the state, they all said the same thing. "We'll re-string it for you if you want, but it happens all the time, we just cut them off at the servings".