He certainly could be a 3rd piece in a bigger trade... or the 2nd chip in a medium-size trade. Individually, I don't think he would bring back more than an A-ball player. I think he's seen in the industry as a quality 4th outfielder. Remember the Twins added him a year ago for a hard-throwing RHP who had not thrown a pitch in the US yet. His value is certainly a little higher this year, but I don't think it'd be significantly more.
The question I would throw back to you all is this: I think we can all agree that if a team is insisting on Cave or a trade won't be made, you add him to the deal. But if adding him doesn't bring back a meaningful return, then what? I personally would rather keep him in AAA and if one of the three starting OF get hurt, he can provide more value to the Twins being really good depth playing well in AAA.
I think he even has one minor league option remaining* after this year, and that's part of his value - his stashability at AAA for this season and next. That would be of value to another team too, so maybe his trade value is a little higher still, because of this, than for a typical 4th outfielder like Robbie Grossman who is out of options. He won't bring back a difference-maker by himself, but should be more than a throw-in, for the right team.
He's valuable, so to answer your question, I'm not in a hurry to dispose of him. But I'd make him super-available, if that makes sense.
* Cave seemed to be injured soon after signing, and missed a couple of years before playing minor league ball in earnest, and I don't know the rostering rules well enough to know for sure that this is the reason he apparently didn't have to be added to the Yankees' 40-man roster sooner than they wanted.