Old English scearn "dung, muck," from Proto-Germanic *skarnom- (cf. Old Frisian skern, Old Norse skarn, Danish skarn), a past participle form from *sker- "to cut" (see shear). Cf. Old English scearnbudda "dung beetle," and Scottish Sharnie "a name given to the person who cleans a cow-house" [Jamieson].
sharn is the common name of cow-dung in the North: therefore Shakespeare probably wrote sharn-born.