Really!?!? Wow...
I would suggest wearing the swim trunks under some shorts and not going in the dressing rooms.
What do you do when he has to go to the bathroom?
And I am sure the women are REALLY going to understand a 7 year old boy seeing them naked if you take him in the women's room! At 7, I definitely knew that girls were different and seeing a bunch of naked women? I would have been like the dancing banana man!