You likely wouldn't be trading for Romo's current contract. You likely could negotiate a restructure. Tennessee did that when they initiated a trade with the Eagles last year.
Regardless when Mike Glennon gets $15MM a year, Romo's $14MM ain't so bad.
Why would an NFL player restructure his contract to take less money if a team just traded for him? His new team would have no leverage at all after trading for his contract. It's not just about the salary cap but also the money.
Players restructure contracts to get future money up front as a signing bonus or to get an extension. His new team is not looking to rearrange his contract or extend it. They are wanting to sign Romo to a lower guaranteed contract with incentives based on playing time.
Romo (nor any NFL player) is not going to tear up their current contract for less money unless they are about to be cut and given an option to take less money to stay. In this case, if a team trades for Romo, they are not about to cut him, since they actually wanted badly enough to trade for him, so there's no reason at all for Romo to take less money and the Texans are not going to want to pay him a lot of guaranteed money or extend him past his 40th birthday. Otherwise, they would be better off just keeping the current contract and seeing how he plays in 2017. At least with the current contract, there's no pro-rated signing bonus for them so they could go year to year.
Given that there's no guarantee Romo will last a full season, and he's going to be 37 years old this season, it would be foolish for any team to trade for him at this point even if the Cowboys didn't ask for anything in return. The contract itself is the barrier more so than the picks.