Any of the small battery powered fans will work fine.
On a broader level, there are lots of ways to try to stay cool. We're big fans of WDW summer, so deal with it all the time. Suggestions:
Avoid the attractions that have outdoor queues during the heat of the day. Thinks like BTMRR and Tomorrowland Speedway come to mind. So many attractions at WDW have a/c, so those are the ones to do during the worst of the heat. Philharmagic, Dinosaur, Nemo, Muppets, Soarin', Living w/the Land, etc...
Wear light clothes.
Drink plenty of water - all the QS places offer filtered ice water for free. Use it.
Some people like
cooling towels. That's a personal decision. Try them and see if you like them. I find them gross and they just make the heat problem worse. WDW is already hot and humid, putting a wet towel on you just makes that worse. Sure, it's cool for a little, but that wears off real fast.
Some like misting fans. Try those. My feeling is same as the towels...they're gross and make things much worse.
Really, for us, it's just being mindful that it's hot outside. We do the a/c attractions during the heat of the day (this is the biggest factor), drink lots of ice water and don't rush. We find that to be more than sufficient to help avoid melting in the heat. During June/July from about 10am to 4pm, we're mostly only out of the a/c to go from attraction to attraction. Only outdoor ones we tend to do then are the water ones such as Splash (with FP+, the queue is HOT) or Kali (ditto).