It's possible. Mummification can be pretty intense but if the goal is to prevent all squirming a lot of it will depend on what the Mistress is wrapping you onto -- which of course is limited by what happens to be in the dungeon. CBT chairs and medical chairs usually work great. A St. Andrew's might work depending on whether there's enough space between the cross and the wall to slide a roll of plastic wrap through.

Either a bonus or a negative, depending on you: the plastic wrap prevents/reduces marking significantly.