What I usually do in this case is redline the contract and sign it. (Meaning, edit the clauses you don't like in an obvious fashion. Tell them you've done this.)
They will often not want to go to the trouble of going back and forth with the contract and will just accept it.
Pretty sure you don't have to tell them if you return the contract to them modified and they sign it. They weren't going to tell you all the objectionable parts of the contract, so why give them information you're not required to give?
IANAL either, but from experience everything that can be seen as shady is very dangerous if it comes to a court case. It makes you look like the bad guy, and can easily be used by a good lawyer to remove focus from what should really matter.
You want everything to be as clear as possible, and with no obvious points that can be called into doubt. Even if you end up winning, you don't want a court case that drags out for multiple years, with devastating legal costs to cover while its going on.
They will often not want to go to the trouble of going back and forth with the contract and will just accept it.