True, although I believe once you waive your NTC to move to a new team it is no longer valid once traded.
I think the Rangers can trade him to whoever they want now. I could be wrong though.
I think you're right, but can't find much to back it up at this point. I seem to recall seeing something a few years back that says that a player who waives his NTC/NMC effectively voids the clause. However, I did find this snippet on CapGeek
If a player waives a clause to accept a trade to a new team, it is rare he will do so without a promise that the acquiring team will continue to honour the clause. Brad Richards, when traded from Tampa Bay to Dallas in 2007-08, is an example of this. However, if the player is traded before a clause has kicked in, that clause is automatically ruled void.
If a player still holds the NTC/NMC with the new club, then why would he need a promise from the new team that they will honor the clause? I could be reading it wrong, but I think that goes to show that the clause is considered void, once the player agrees to a trade.