Dropping off is a good option for many people. Each park has a drop off area; ask at entrance booth.
Whether there are handicapped parking spots close by depends on when you get there.
If you are going at park opening, chances are good you will end up in one of the closer designated handicapped parking spaces. The lot is long and narrow, so the farthest spots in any of the park’s handicapped parking can be a bit of a hike. If you are later, you may end up in the Medical Overflow area. In each park, those are beyond the marked handicapped parking area and are regular parking spots without space on the side for transferring.
The designated spots are marked with blue painted lines and/or signs. Guests parking in those designated spots must have a valid handicapped parking permit or could be ticketed.
We just got back from a long trip to WDW and usually drove to Hollywood Studios when we went.
We were not able to get there early and usually ended up in the Medical Overflow lot rather than the actual designated handicapped parking spots. That was an issue for us because we need to be able to park DD’s wheelchair next to our vehicle and lift her in; we sometimes had to temporarily block the lane to have room to safely move her.