The Sefer HaChinuch (Mitzvah 552) writes that, while according to Halacha Kiddushin can be performed with any marginally valuable item, the custom is to utilize a ring. The reason he gives is that it serves as a “constant reminder” to her status.
All the moreso a sheital or hair covering, which is halachicly obligated and thus expected to be found on a married woman’s head must be noticable.