It's hard to know which GM, if any, wants Swihart, and if one or more do want him, they may be waiting (hoping) we just DFA him at some point, and they can get him for free.
If it was me, assuming we do not want to go with 3 catchers, I'd trade him for the best we can get, even if I think he's better than what we get back. Get it over with. DFA him, if nobody wants him.
(I'm okay with going with 3 catchers, since Swihart offers some depth at other positions, and Pedey's health is highly questionable.)