Boardwalk and Beach Club are fairly close to walk to. I've never at the Beach Club's QS, but I know you can get allergy free chicken tenders and I believe also allergy safe Mickey waffles at Cape May Cafe. Kouzzina (sorry another table service) also has the Mickey waffles there too.
The only place I've been to at the Swan and Dolphin is Fresh Mediterranean, it was good and they accommodated fairly well, but it's TS.