My former husband and I were both in recovery when we got married and this question came up.
What we did was have a small (mostly family) morning wedding (10 am) followed by a brunch and a cash bar. I don't recall even seeing the alcohol and as far as I know, most people there weren't into drinking much at that time of day.
My second wedding was even smaller, in a park, followed by a family barbecue at my brother-in-law's house. There was no alcohol at that one.