Obviously there might be context missing that makes "approach them and make your intentions clear" more risky or intimidating, but if they help you directly you could just propose getting a drink or something if you were having some good banter, like "this is fun and I enjoy talking to you, wanna get coffee sometime?" Or whatever.

If you both are nervous and struggle with the banter you could go the middle school route and like, slip them a note or something with your number and that you want to hang out sometime. You probably already thought about both of these methods though. Sorry if I'm not helping.

Downside of acting on the impulse is that it might be awkward getting service from the deli if it doesn't go well. Have a backup grocery store I guess? I think that can be helpful though, keeping the stakes in mind and not letting your mind run wild with exaggerated fears. Worst case scenario you're where you started, except maybe you go to a different deli.