If you want to wear a fanny pack, I agree with PP and say wear what you want and don't worry about anybody else. People at Disney are focused on their own concerns and their own fun, and probably aren't taking the time or energy to judge what other people are wearing.
But I think fewer people are wearing fanny packs than in the past, which may make them harder to find if you are shopping for one. If you aren't looking for one with a pretty print, maybe see if you can find one which is being marketed to men? I would think that if it's a solid color, it wouldn't seem masculine or feminine. I hope it's not hurtful for me to say that. I'm someone who likes a neutral solid color for my bags. But I know other people who prefer Vera Bradley or something like that.
I switched from a fanny pack to a tote bag when I started carrying more stuff around with me. Cell phone, portable charger and cable, sunglasses, wallet, lip block, sunscreen, hand sanitizer, tissues... a tote bag works better for me. I like the LL Bean Everday Lightweight Tote in medium size.