From a paean to etymologist Gerald Cohen over on Tablet:
His first major endeavor in this field, beginning in 1976, was a seven-year effort to clarify the origin of shyster. After he had begun his research, Roger Mohovich of the New-York Historical Society drew his attention to newspaper articles in 1843 about the Tombs, the city prison. Editor Mike Walsh denounced scammers who took prisoners’ money by pretending to be lawyers who would get them out. One of the scammers who actually knew something about the law disparaged his rivals by calling them shisers, British criminal slang for worthless people. (It comes ultimately from the German word for excrement.) Walsh misheard it as shiseters, and a new word was born.
In day-to-day talk, I enjoy calling people—even non-attorneys—shysters. Now I can do it with the confidence that "shyster" doesn't just mean "bad lawyer," it means shithead in general.
A slightly more direct version from the Online Etymological Dictionary:
"unscrupulous lawyer," 1843, U.S. slang, probably altered from German Scheisser "incompetent worthless person," from Scheisse "shit," from Old High German skizzan "to defecate."
I always thought "skeezy" was a mashup of "skanky" and "sleazy," but now I wonder if it has some roots in "skizzan."