So I have a tiny bit of the wrap peeling off around my hook keeper, could I brush on a small amount of epoxy to prevent further peeling? 

Just my opinion but if it were me,  I'd find a store that does rod repair and let them deal with it.  Shouldn't cost more than $15. Just wait till winter when you don't need the rod.   It will be just fine till then

Mudhole sells the rod epoxy, but it is runny and the rod will have to be turned in a turning device continually until it dries to prevent a blob.  A rod repair service will make it look like new.

Yes.  I recommend, if you want to do it yourself, flaming the thread fuzzies, then clean the surface by gently rubbing with fine steel wool, or preferably, Scotchbrite pad.  Wipe clean, no alcohol, and apply epoxy.  A light coat will unlikely cause a blob, but to be sure, just turn it every 15 minutes until it's jelled.   Check its condition by touching the epoxy in the mix container, not the epoxy on the rod.  With the color of the thread, and the fact that it is such a small area, any liquid epoxy will work just fine.  Thin coat!