I was lucky mine was done while I was at the hospital, they just put one of those toilet dome things under the seat, I went, then a nurse came and took it away, couldn't complain :P
I remember having to do them at home by myself though, I was very careful. Spooky I did the very same thing you suggested with the plastic wrap when I did it years ago, someone else suggested it to me and it worked very well. Not only that, and most importantly it made it less gross and a lot easier clean up.