"You shall not wear": This tells me only of wearing. Whence do I derive that he may not cover himself with it! From (Vayikra 14:19) "and a garment kilayim shatnez shall not come upon you." I might think that he may not throw a bundle (containing shatnez) over his shoulder (to carry it); it is, therefore, written "You shall not wear." Wearing was included in the general interdict (against shatnez). Why was it singled out (for special mention)? To use it as the basis for a comparison, viz.: Just as "wearing" is distinctive in that it is of benefit to the body, so, all that is distinctive (is forbidden by reason of shatnez, to exclude throwing it over one's shoulder).
What Is Shatnez and Why Is Mixing Wool and Linen Forbidden
Sifrei Devarim 232:2