OKW Lover is correct. You do not need to push the chair up the hill. You can take the path by the water, where there is no hill. This path crosses under the bridge, rather than angling up toward the bridge. You will see the path on the left as you pass the boat dock.
The choice you will have is either pushing the wheelchair from the boat dock along the water to the Beach Club, into the Beach Club pool area (this is accessible by entering the lobby and walking past the Cape May Cafe, then exiting the building again by the pool) or taking the boat, which will stop at the Boardwalk before continuing to the Beach Club, then pushing the chair down the Yacht Club pier and approaching the pool area from the Yacht Club side. Either way is just as much walking, and it may actually be more walking if you throw in having to traverse the Yacht Club pier. If you have time and you'd like a boat ride you can do it that way, but it is just as easy to walk it without taking the boat in my opinion.