Does Zed Without a Sound swap locations with a shadow clone?

Yes. Zed, Without a Sound's ability reads "Move me and a Shadow Clone you control to each other's locations," and the Shadow Clone token (from his conquer trigger or Death Mark) is a unit named Shadow Clone that you control — so it's a legal choice.

This works even mid-combat: the swap moves Zed into the clone's location and the clone out of combat, dropping its Attacker designation (FAQ #11820). Both move simultaneously, and neither relocation is a Standard Move, so no move restrictions apply.