Gauze Compression Garment and Chin Liposuction (post-procedure)

I've gotten some quotes from places that do chin lipo. Most offer a compression garment to be worn as much as possible for a few days, then when you are going to sleep for a couple weeks. one of the places I am looking at wants me to wear a gauze wrap around my entire head for a week b4 switching. Would it be fine to do this but just buy my own compression garment and use that instead of a gauze? That way I can shower, walk my dog for a bit, grab food, and still have the wrap on for 22/24 hrs.