My question: can they be married by a justice of the peace? Would the JP be called a preacher or a reverend? The girl is Episcopalian and the man has no religion to speak of. It's imperative that the wedding take place immediately, so if there's a three day waiting period, that's not going to be good. I can have the officiant be friends with the male character and do him the favor of rushing it.
Searched: Mid-/1800s Civil War Era Marriage Proposals.
Wedding Customs Before the Civil War.
New York Marriage Licenses 1860.
Antebellum and Civil War Weddings.
The thing is, these expect the weddings to be elaborate occasions and not something rushed to protect the bride's reputation.
I also checked out the tags in this group (and found a very interesting one on crossdressing, which should come in handy down the line in this story.) but nothing addressed this particular topic.