Mud wraps are often (but not always) applied with brushes, however it may be suifficient for you to say "mud wrap" or "mud body wrap" unless it's important to specify the application technique.

see
http://www.dietspotlight.com/sea-mud-body-wraps-review/
where it says:
Sea Mud Body Wraps are marketed primarily to women who are seeking assistance with weight reduction and skin detoxification. This beautifying treatment contains bromides, potassium, magnesium, sodium and sulfates to potentially draw toxins out of the skin, tone the body and aid with fat reduction. This treatment is applied with a brush on bare skin,

and
http://www.ehow.com/way_5325592_body-wrap-techniques.html
where it says:
With a mud wrap, the warm mud is applied to the body, usually with a brush, in a thick layer.

and http://www.torfspa.com/body_wrap.html
where it says
Brush the paste on the body in an even layer starting from the feet up.

and http://skincare.lovetoknow.com/Body_Wrap
where it says:
Mud Wrap
The mud is rich and warm, the experience exceptionally soothing and nourishing. Similar to a mud bath, the mud wrap involves slathering the body with the thick substance (it is typically painted on with a large, gentle brush)