My husband and I did a similar celebration (now 30 plus years ago!) We had an intimate ceremony and dinner Friday night for our immediate families, plus a couple close friends. The next day, we had a picnic type backyard party with volleyball, caterer, DJ etc. We sent party invitations that had an official wedding invite look and RSVP card, that alluded to a wedding celebration, by mentioning wedding cake and champagne toast in the “please join us” part. Because the picnic was Saturday, most people just came to town for one night. No one seemed to mind at all. We just told them verbally, if they asked, that we wanted a private ceremony and they seemed to understand. I put on my gown for a hot minute to cut the cake, and let them take pics, then it was back to shorts and bare feet. The people I know are more interested in the party than the ceremony anyway. We ended up having an impromptu after party when people wouldn’t leave. Enjoy your day! It sounds fun!