Sounds good. We use the small rolls of wrap but never go around any part of the patient, always along in strips overlapping as needed.
Try doing the cling film as you describe in a dry run and video it. then look at the video and see how you tore the cling film, what the cling film touched and ask yourself was that a "clean" procedure? most people will put cling film onto a table, rest it on kit, leave the roll open, and i have even seen the cling film placed on the floor to cut it.
Not very hugienic and a great introducer for Bacteria to a wound site.