That's the beauty of atomic swaps. There is no exchange. It's trustless and decentralised.

The only tricky bit is plausible deniability on the CBDC side, because obviously they'll profile addresses linked to anonymous swaps, so you need some type of middleman wallet so you can just say "I sent someone some money, what they did after I don't know, and I don't know what you're talking about."

It'll get worked out some way or another. Atomic swaps between blockchains are already possible. CBDC implementations are being designed already iirc.