“Şalvar” was not the generic word for trousers! It was one of several styles of pants, and an unpopular one at that.
The available definitions are predictably maddening. In a 1533 dictionary, şalvar are defined as “chalzoni grandi oue a chammino si mettono le ueste” and in 1611 as “weite hosen wür (!) frauen,” wide trousers for women.
The derivation is the Persian šalwār, “inner breeches, drawers reaching to the feet; sailor’s or traveller’s trousers.”