Well on my first Disney trip about 10 years ago, I called a cab company and asked this very question. I was quoted $30 RT from All-Star Sports to Wal-Mart, 30 minutes waiting, and back to All-Star Sports. I haven't checked since, so I was guessing a minimum of $40.
I think I would rent a car for a day from the Dolphin or Car Care Center at Disney, that way you can take your time and have what you need for the trip.
However, if it was me, I would rather pack it in checked luggage, or have it shipped to myself to save precious vacation time. (I have done both and it worked beautifully).