Currently, online stores do not have the ability yet to add surcharges. It may be coming or not, I didn't see a mention directly in the upcoming features in a glance. If you really want to get that credit card processing to be paid by the customer, then adding it into the item is your only current way. A side benefit is that you can only charge surcharges on credit card transactions, but by including it in your price (like you should be adding your labor, item, property taxes, utilities, overhead, etc.) is that you get it on all your transactions.
https://squareup.com/help/us/en/article/8596-set-up-and-manage-card-surcharges
