What shoe is better, cross trainers or walkers?

Hi! I have a trip coming up to Disney World. I have REALLY high arches and get a lot of arch pain, especially when walking a lot at Disney. I wear arch supports and they do help a lot. Conversely, when I am at home, I work out a lot in the gym. I get my cardio from an elliptical, but don’t do a ton of walking. Maybe I am being cheap, maybe I am being practical, but I would hate to buy two kinds of shoes. Could I kill two birds with one stone? What do you think?