How many of the kids would quit buying your special if you did put in a minimum charge?
You may be losing the whole $4 sale rather than the 22 cents. If your numbers show you that you would be better off with a $10 minimum that is what you should do. My numbers have shown that even if the charge is only for a small order it is worth my while even with the CC fees.
I believe the old saying is “Never trip over a quarter to pick up a nickel.”
I don’t know your cost structure on the slices, but if I were to do a 16" 1-topping cut into 8 slices, those two slices and drink would cost me about $1.05. I’d gladly take the 22 cent hit on that margin if it keeps the kids coming in. Darn, I wish I could sell 50 of those per day… but I’m not in a location for that type of business.
Are you able to take PIN debit? That would reduce that cost at least a little bit. I have to assume that “kids” are using a debit card and not a credit card.
I would probably just raise your price on the slice special by a quarter. Not that I speak for every customer, but personally, I always roll my eyes when I see minimum card amounts. Mainly because I always seem to be short of hitting that minimum - then am forced to decide between purchasing something additional I really dont want, or just leaving. Its too big of a gamble to take bud!
Another option is to make your special 4.50 and then have a sign offering a discount of .50 for cash. That way it looks more like an opportunity for savings rather than a penalty for using the card.