This is the right county for Esbjerg, and I was hoping someone might reply to you with an answer. I don't know how to find someone in the time period that you're talking about, when the records are still private, I think. If I were you, I would join the Danish-L genealogy list, and ask about it there. To join, go to www.rootsweb.com, and click on mailing lists, then go to International, then Denmark, then, Denmark-L . Also you might write to the Lokal Arkiv in Esbjerg. Here's one that I found using google:
http://www.esbjergbyhistoriskearkiv.dk/ . Let us know if you have any success.