I think the most effective thing you can do is to ask for testing on the day of. To be courteous, I would offer to provide free rapid testing on site (a half hour or so before the event) for those who don’t have access to a test (although most people should).
Personally, very recent testing makes me feel far safer than vaccine requirements. I recently got my 4th shot, so obviously I believe in vaccines. But with the high rate of recent cases, I think the whole situation is far muddier than it was a year ago. Now, I’d rather sit next to an unvaccinated person who recovered from Omicron 3 weeks ago than a vaccinated person who had their last shot or booster 6 months ago. It’s just not as clear as it used to be. It seems that most unvaccinated people have recently had Omicron. So require vaccines if you want, but I doubt that adds too much protection these days. One thing I would never do: require guests to upload their vaccine card. I would do that for a work event or other non-personal event, but not for loved ones I’m inviting to my wedding. It seems cringey to me to imply you don’t trust the kinds of people you’d invite to your wedding to be honest about their status. So even if asking only vaccinated people to come, I would hesitate to have an upload feature. I am sure other people may feel differently, but as an event amongst loved ones, that strikes me as icky.
I think the best protection you can offer your guests:
*. Day of testing for everyone (BEST and most effective rule, IMO)
*. Excellent ventilation, including as much outdoors as possible, as much open windows as possible, and pony up for major league HEPA filter air purifiers to put throughout the venue. Perhaps you can borrow some from friends. Very good ones are available on amazon for approximately $250 each; I would think you’d need several of those for a wedding venue.
*. Ample spacing. At my wedding 28 years ago, we got too many rsvps and crammed people in there 
. You can pointedly do the opposite. Provide a space far bigger than required for the number of guests, so the tables can be amply spaced (both spaced away from other tables, and hopefully have only 8 people sit at a table that might be able to accommodate 12).
By the way, I love places (restaurants, homes, etc) where people make it clear what the ventilation/filtration situation is. There are a couple of local restaurants that have very obvious air purification units visible to all, with signs that explain their ventilation situation. I love that, it gives me a lot of comfort. So if you do bring like 10-15 units with you, on your card that asks people to do day-of rapid testing, you could mention that you will be providing enhanced air filtration and ample spacing. It seems gracious to offer up what YOU are doing to increase safety, while asking a favor of your guests.
I think much of the safety is under the hosts’ control, especially in terms of ventilation and sufficient spacing. Then, pray for the best!! BEst of luck, this is such an exciting event, I hope you can fully enjoy it, hooray for your family!!!