Hello @gingeraz thanks for your post. Yes, you can use a Square reader to process credit card payments without having setup a website. Just be sure you have your account settings current for your banking info. You do not want to accept a credit card payment at your craft fair and then not be able to transfer that money into your bank account. Check this post to make sure your account is still setup and ready to process payments.
You should also consider upgrading from the standard mag-stripe reader, to a contactless/chip reader. It's so much easier to accept a credit card and you can also accept contactless payments from a person's phone. Also by using a chip reader you can better limit your liability if fraud should occur.
