Thanks to you both!
When I decided to do this tune I looked around on youtube to see who else had done it on uke, to get some ideas. I did find one good example, but was surprised to see he had opted to play it in the original key - Eb, which doesn't seem like a very natural key for uke. However, after some experimentation I found that Eb is really the only key that makes this tune possible on uke! I probably should include a link to the version I found on youtube, but I don't have it any more. Anyway, a testament to the power of youtube and of course, Stevie Wonder for writing such an awesome piece!