We've also done WDW just after the 4th and I don't think that it's THAT bad. Yes, it's hot, humid and crowded. But the parks are open longer, shows like Fantasmic! and Spectromagic run more often, and the attractions with multiple tracks have them all open to move the lines more quickly.
We take plenty of water and a MistyMate. We tour the parks as soon as they open, use FastPass to our advantage and get indoors before the afternoon heat sets in. At sunset, we return to touring the parks. If you think like a Florida resident and avoid the heat of the middle of the day, you should be okay.
While it's not my favorite time of year to go to WDW, it still beats a week in Philly.