Bran, I’m from a similar position, I like paying in cash. I always have cash € and $ with me, and a zero-foreign exchange rate card in my wallet. I do the math, and pay in the manner month advantageous to me. Sometimes, it’s not why I expect.

Sometimes that’s cash €, which at a 1.12 exchange rate, and a 3% surcharge would cost me $1.15 out of an island ATM. NEVER buy € in an airport.
Sometimes that’s cash $, when there’s a 1:1 , or if the restaurant’s exchange rate favors $.
Sometimes I just pay with no-fee plastic.

Keep in mind that businesses, other than currency exchanges, aren’t in the currency exchange business. If they accept $ then they are actually doing you a favor, so the current market exchange rate shouldn’t be expected.

Example: Current rate 1.12. Restaurant rate 1.20. ATM/Credit card 3% fee. ATM/Credit card 0% fee. €100 restaurant check (Easy number to work with.)

€ $115 € from € in your pocket from an ATM
$ $120 $ from the $ in your pocket
$ $112 $ on your credit card with a 0% international fee
$ $115 $ on your credit card with a 3% international fee

For some, the small difference doesn’t matter. For others, budgets are tight, and every $ matters,

PS - Never trust my math, 😝, double check it yourself.