the kids shoud not be doing this. the coaches should. and certainly there are doctors/parents at these gyms that can show the coach how to do it.
crazy glue has been used for ions in gymnastics. they use this product today in hospitals as an alternative to stitches/staples to closing small wounds. and i certainly did not imply to pour crazy glue into an open wound.
i understand your staph episode. the problem today is that the gymnasts [or coach] rip the flaps off. then put dirty wrist bands back on over the wrist rips, or grips back over and on the open rips, along with spraying water from the water bottles, and spitting, and so on. you get the message.
then, the parents put neosporin/biaxin products on the rips. and usually without cleaning the wounds sufficiently and giving them time to dry out. skin growth is expedited by those products giving a false sense of there being enough skin growth to continue on only to rip worse and usually deeper within 72 hours. and as coaches know, this always happens on the eve of competition.
saline solution and vaseline are best post rip. and again, one's own skin is better left on the wound for expedited healing.
someone posted electrical tape. scotch tape is best. some tapes have adhesives that could be caustic and irritating and prolong the healing process. though you must use more of it, scotch tape has not caused any problems for those that use it. and i'm sure that will be said for electrical tape as well by some that use it. and scotch tape can be place on those little 'tags' of skin you are speaking of.
my above recommendations are not mine exclusively but those of a dermatologist.