If one has a mixture of different hand towels and would like to separate one to put away for later, this would seem to be a problem of borer. Would an acceptable solution be to wash one’s hands (even if they are not dirty and one would otherwise have no reason to wash them) and then retrieve the desired towel and dry one’s hands on it? It seems that this might be a fulfillment of the requirement of miyad by borer, since the towel is immediately being used for the purpose of drying one’s hands. But would it be permitted to do it in this way?
It sounds very correct, as you so nicely wrote, since you are using the towel for right now, it is permitted to separate it. Once it is separated you can put it in away for later.