With a skin graft, do you have to wear a compression garment?

Not usually. I do not ask my patients to wear a compression garment once their skin graft has completely healed. While it is healing in the short term (the first week), i usually do have some compression applied to the graft, if possible, to help increase the likelihood that it will take.
Yes . You really should once the graft has taken and is healed initially. It will improve its ultimate appearance greatly.