I would go resort hopping and enjoy the ambience of the lobbies at the Poly, Contemp, Wilderness Lodge, and Grand Floridian. Use Disney transportation (buses, boats, monorail) to enhance the experience.
Enjoy a 15 minute sit break in each lobby. Browse the shops. Indulge in an ice cream bar or a Dole Whip (at the Poly). Relax.
Not much shade at the pool. IIRC there are a few umbrellas and the side over by the slide can get shade from the trees behind the walkway at some points in the afternoon. I'm sure these will be crowded though.
Bama Ed
PS - one of my favorite places is the Golden Spike Room (or whatever it's called) over at Wilderness Lodge DVC. At the WL bus stop, follow the sidewalk down to the right and you can enter the door just fine. Walk forward into the small round lobby and the GSR is off to the right. Chairs, couches, a checkerboard, it's nice. (It had a fireplace burning when we were there in March - don't know if it would be burning in July). Bring a book or something else to do and enjoy. They have momentos and pictures from Walt's backyard railroad. It's pretty quiet too.