Tiny Ceremony Larger Reception

My friend did the same, small ceremony and large reception and they did two set of vows.

Their personal one with family and a second with friends and family.

Your DJ will likely introduce you as the newlywed couple as you enter the hall. And if you're doing speeches at the reception, I think that'll be enough. The only thing they literally miss out are the formalities. But if you really want them to be part of the "ceremony," you can have the videographer edit a highlight reel the day of and show it at the reception. It's a fairly pricey option though (makes sense since they have to edit one thing while simultaneously shoot your event).

Live stream? or have small video snippits to play at the reception.

or if you have a couple of funny friends have the reenact it thinking olaf telling the story of ana and elsa from frozen 2 LOL