I think the easiest way would be to put a card reader into a laptop and set it up in a kiosk. There are ways to script behaviours to be triggered on the insertion of a card, USB stick or other drive type - you would simply pull all the data off the drive on insertion, with some feedback so that you know when it has finished and how long it is going to take. This is really all that is going on in the photo-printing kiosks, but you could set up yours to be simpler and less discriminating. Note that this can present challenges with, for instance, very large cards, or cards with other photos on them. One way around it would be to plug in your card, have the computer read the card and display a message like "Found 14 photos taken today - Thank you!" and then "Downloading photos ... 10% ... 20% ... 30%..." etc.

Note: At my wedding we also skipped having a photographer, and we learned some important things.

1. You need a photographer wrangler - someone to arrange which lens the subjects of the photo are supposed to be looking at - otherwise you get shots of the bride and groom looking in opposite directions in out-of-sync smile cycles.
2. Make a list of the photos you want to have in the future, and make sure the photo wrangler has that list and the force of personality to get it executed.
3. Volunteer photographers have less patience - be organized, loud enough to be heard and make sure you get the shots you want without ruining the flow of the day.

Good luck, and congratulations!