I’d be totally on board with getting married privately and having a big party later. In this case though I’d advise against it. Assuming you’re getting the greencard process started after you’ve eloped, you’ll need a certain amount of letters from friends and family stating that you guys have been a couple and are legitimate. These letters seriously can look like school essays describing your relationship from the eyes of “witnesses”. I got my greencard as well, so I’ve been through it. It would look real odd if everyone talked about you as engaged.
Just tell people you want to have a small private ceremony and you will have a big party later. If they’re upset, they’ll get over it.