It would depend entirely on who's available.
If Barron, Cox, or DeCastro is available, I use the pick and don't look back. If all three of them are gone, then yes, I'm looking for the best trade down I can get. I'm guessing the team with the most to offer and who seems to be the most interested in Floyd is Cleveland, which would mean dropping down to #22. I think the Cowboys would demand either their second rounder (#37) or their third and fourth (#67 and #100, respectively), with the possibility of taking their third and a second next year.
The Cowboys would definitely be getting the better end of the trade in those scenarios, but it would be a seller's market.