1650s, phonological spelling of chamois. Other bungled spellings include shambo (1610s), shamois, shamoys, shammies. Compare shay from chaise; shappo (1700) for chapeau; shapperoon (1620s) for chaperon.
1550s, "Alpine antelope;" 1570s, "soft leather," originally "skin of the chamois," from French chamois "Alpine antelope" (14c.), from Late Latin camox (genitive camocis), perhaps from a pre-Latin Alpine language that also produced Italian camoscio, Spanish camuza, Old High German gamiza, German Gemse (though some of these might be from Latin camox). As a verb, "to polish with chamois," from 1934. Compare shammy.
Its size is about that of a well-grown goat, and it is so agile that it can clear at a bound crevices 16 or 18 feet wide. The chamois is one of the most wary of antelopes, and possesses the power of scenting man at an almost incredible distance, so that the hunting of it is an occupation of extreme difficulty and much danger. [Century Dictionary]
"do a suggestive dance," 1918, perhaps via phrase shake the shimmy, which is possibly from shimmy (n.), a U.S. dialectal form of chemise (mistaken as a plural; compare shammy) first recorded 1837. Or perhaps the verb is related to shimmer (v.) via a notion of glistening light. Transferred sense of "vibration of a motor vehicle" is from 1925. Related: Shimmied; shimmying. As a noun, the name of a popular, fast, suggestive pre-flapper dance, by 1919.
<a href="https://www.etymonline.com/word/shammy">Etymology of shammy by etymonline</a>
Harper, D. (n.d.). Etymology of shammy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/shammy