Is it the 4th of July weekend Saturday?
If it's not - Saturday's are usually not that bad in the summer. I was there last year on July 14th 9 (my birthday) and July 14, 21 and 28th and it was fine. Granted we went at opening and stayed till closing on everyday except my birthday. The 14th was our first full day of our vacation. We arrived at the hotel on Friday July 13th.
I'm not saying no one was there and it wasn't busy - but for a summer it was managable getting there in the morning. If we were arriving in the afternoon, I would plan on getting FP's if there are any left for the night time hours. Ride things without lines in the afternoon like Mickey's Philharmagic, COP, Hall of Presidents, Etc. Walk around and look at the lines and pick and choose the things that aren't bad. Then hopefully you can ride something later in the evening with a FP. No matter what park you go to you will have a problem.
I'd also pay attention to what park has EMH hours. If MK has EMH hours either morning or late then I would avoid. If they are the day before or day after you are good.