What you really need is a bout "list" instead of brackets. I don't know if TW is capable of producing a list as some other tournament programs do, but that is what you need. That way the match numbers for your entire team would be on one single piece of paper. Perhaps the tournament management could see that bout lists were available to the head coach of each team, prior to starting?
That would be good for the first round, but you will still have to go to the wall brackets after the second round, unless the brackets are pre-printed with match numbers, and no changes made to the numbers. Even then, a club with 20 kids, that is almost impossible to keep up! A good wife with wrestling experience is more valuable than any software program could be at that point.