Akkadian

ḫarāšu - binden, anbinden(?) (CAD Ḫ 95, AHw. 324)

Probably related. In CAD (meanings 3a, b) commented as: “uncertain meaning, said of parts of the human body”. However, at least two contexts clearly refer to mouth.

PS
*ḫrš - to be deaf and dumb (SED I No. 32ᵥ; HALOT 357)