Legally married before wedding. Is it deceptive?

Hi all. My fiance and I got engaged earlier this year in May. We’re doing a smallish wedding with about 50 people. My fiancé is not a US citizen so we are applying for a marriage based green card. After setting the date, we found out one of his close family members was sick. After speaking with a lawyer, we decided it made the most sense to just legally get the papers signed so we could start the immigration process ASAP.

We did no ceremony no nothing. Just signed a paper. It wasn’t really related to the wedding at all in our minds. At the time it seemed normal to us to just not tell anyone and still do the wedding (edit here to say I did tell parents and close friends who are in bridal party). We also didn’t really want to explain to all our friends and family our decisions about immigration. I don’t wear my wedding ring and we still feel like we are “engaged”.

But not as it gets closer to the date I am starting to feel really guilty about it. We haven’t sent the invitations out yet but we did send out save the dates. Should I come clean and tell everyone we’re already married? And just do a reception? I don’t want to spoil the wedding day but I also don’t want to come across as deceptive to any family or friends.

I really don’t know the best thing to do here. Would yo feel deceived if you went to a wedding but found out the couple was legally married a few months earlier?

UPDATE: Thank you for all the kind words and thought out responses. After reading your comments it seems like the consensus is it shouldn’t really matter what day we sign the papers. But I do acknowledge other’s input. It would certainly be appropriate to state somewhere we signed the papers ahead of time in case any friends or family don’t like it, they can make their own decision to come or not.

In my mind we are still having our wedding ceremony on the date planned even though some people say my wedding ceremony came and went and I don’t get another chance. Too bad for me. I guess I am technically wrong but that’s when we’re exchanging vows and rings for the first time so 🤷‍♀️