Keep in mind that to improve your privacy using atomic swaps you'd still need to do the swap with a privacy focused cryptocurrency (similar to what fravia suggested, except without the need for a centralized exchange).
True, but there are proposal/idea to improve privacy when using atomic swap (even though atomic swap itself is still in development) such as Anonymous Atomic Swaps Using Homomorphic Hashing
That's pretty neat!
Thanks for the link, I wasn't aware of this proposal. Seems like this approach could greatly improve privacy even when swapping currencies that are not necessarily privacy focused. The amount of privacy you get might depend on the amount of other users using anonymous swaps though (ie. if it's just you and 5 other guys it might be rather easy to correlate transactions).