Humid? Rarely can SoCal weather be considered humid. I lived there for 28 years.
No, the difference between these two weeks will not matter. We have gone the first week of June the last two years and the daily high temperatures never got above 85 degrees. However, last summer there was a heat wave in July where it 100 degrees at DLR on a number of days, so the potential is there for significant heat. And then the bulk of your park time will be during those glorious mornings and evenings where temperatures are in the 70's.
HOWEVER, if you get a nearby hotel and take a swim and nap break every afternoon during the hottest part of the day, any heat that exists will not affect you very much.
I believe there are shuttles from the airport, but have never used them so others will have to pitch in here.