I use a hip bag with leg strap for theme parking and
especially for HHN. This is the exact model, looks like it's not available anymore but there's plenty like it on Amazon. I prefer the vertical design to a fanny pack because it's deep enough to hold any of two of water bottle/umbrella/blinky cup at a given time, in addition to battery pack/sunscreen/keys/lanyards/etc. It's unobtrusive, hands-free, and not especially sweaty.