One of my mentors told me a long time ago not to handle bats, helmets, etc., during the game. not only to avoid situations like this one, but to avoid the appearance of favoritism.
If I pick up Team A's bat and hand it back to a coach after the half-inning, but I don't do it for Team B for whatever reason, now Team B can think that I am "favoring" Team A.
Yes, I realize this sounds silly, but I think we have all seen how warped little coach's minds can work sometime.
So maybe I will come off as a jerk for not helping out with the bats and helmets, but as long as both teams think I'm a jerk, it's all good.