Lots of players are reasonable about the business side of things. Its not exactly unheard of for a player to waive a no trade clause, not to mention not doing so with his team in the position, quite possibly directly leading to another (better) teammates life being uprooted, when it otherwise wouldn't have been, can make this "awkward"
Its not like their aren't a number of legit teams out there, especially seeing how Isles and Dallas went far, he can give them a narrow list of solid teams and keep both sides relatively happy. He could end up getting more ice time as well on another team. Players want to play. If Tampa has a number of better players, getting even better, his time can shrink
*also, if I'm not mistaken, they could just buy him out which could create more "awkwardness" if he knew he was leaving either way and forced the worse option on them, out of what could be perceived right or wrong as pettiness.
I don't for sure expect him to waive, but i would not be even slightly surprised if he does.