//AFAIK the difference is the patriarchal nature of the wedding ceremony, i.e. it's based around the traditional concept of a woman supporting a man.//
You can changed the wording , can't you to what you want , providing that the following is included , as far as i am aware
"I, (Bride/Groom), take you (Groom/Bride), to be my (wife/husband), to have and to hold from this day forward, for better or for worse, for richer, for poorer, in sickness and in health, to love and to cherish; from this day forward until death do us part."