Romos contract is not an issue for the team that receives him because nothing is guaranteed.
His base salary is 14M in 2017, 19.5M in 2018 and 20.5M in 2019 and none of that is guaranteed by the team taking on the contract so Romo will happily rework the contract for some guaranteed money and bonus $$ up front or the team can leave the contract as is because if Romo meets expectations, the salary would be under market and if he doesn't, they can cut him.
The hurdle to the trade is that Dallas has to eat all the dead cap of 19.6M for bonus money paid whether kept, traded or cut and if traded, I think the entire amount hits the 2017 cap vs a June 1st cut allows it to be split over 2017-18.
IIUC, Romo is a vested veteran, so if he is cut/released, he is not subject to the waiver process and can negotiate with any team he wants**
Since Romo is likely to cooperate with the Cowboys, a trade could be worked out before the draft, then the Cowboys could make him a June 1st cut (assuming its kosher to have a gentlemen agreement with the trade partner that the terms of the trade still apply after the cut). This would allow Dallas to spread the cap hit over 2017-18 at approx 9.8 Million per year.
I don't know if its allowed but if it is, I'd see if Romo would agree to give back the bonus money Dallas has paid him in an amount that would equal the amount of the signing bonus received by the other team (which would cost him nothing, its merely transferring the guaranteed money to facilitate a trade). Let's say this turned out to be $10 million which would reduce Dallas's dead money hit down to 9.6 million which would really come in handy. Not easy to pull off even if its allowed but it doesn't hurt to shoot for the stars.
** per
this article:
Once the waiver period starts each year through the trading deadline, a vested veteran — a player who has acquired four years of pension credit —
is not subject to the waiver system if the club decides to release him. That means if a team decides to release a vested veteran, the league considers his contract to be terminated immediately and he is free to negotiate and sign with any other club. From the trading deadline through the end of the regular season, vested veterans are subject to the waiver process.