I am BT that was married (to a Jew but not in any religious ceremony) before and later got divorced. I asked R’ Shlomo Zalman, ztvk”l a shaila about covering my hair and was told that I do not have to cover it before I married. It is a chumra to cover the hair if not married/divorced with edim.
I got married in Yerushalayim and, according to the minhag here, covered my hair before the chuppah. It was simply easier to put a shaitel on before the chuppah and have everything ready rather than doing it in the cheder yichud. I have seen kallos from chassidishe mishpochos with their special sequined tichels for after cheder yichud and I also saw a kallah who kept the covering on over her hair (showing only her face after the chuppah) and put a shaitel on in cheder yichud.