Before the ATM was installed, we always used to take a mixture of euros, sterling, travellers cheques, and debit card and we would ask either Olga or Philip (Tria) to change our travellers cheques, and Olga for the sterling, or card. There were plenty of other places to choose from in Arillas that would also do it.
Unless things have changed in the last couple of years, I don't think getting euros will be a problem without the ATM.