The OED, Oxford English Dictionary (should be on every material culture
specialist's shelf) sheds little light on derivation but has Jew's Harp
 documented from 1595 onwards. It suggests derivation from jaw harp is
unsupported and that the Jewish association is only found in England. The OED
conjectures that they may have been sold or imported by Jewish merchants,
thought to have been so or that it was a marketing ploy linking them to
biblical instruments. The alternative name of Jew's trump (from Trench
trompe)  is documented from 1545 onwards. The 1545 ref is from the Rates of
Customs: "Iues trounks (Fr trompe also = elephant trunk) the grose iiis
iiiid".
Paul Courtney, Leicester, UK