I would not sign such a document. There are plenty of great clients out there that will not put you through such headaches. Choose one of them.
If you really want to work that contract, I recommend giving them a link to Upwork's TOS and ask them what they find lacking. Sometimes clients will propose an outside contract because they have no idea what protections are included in Upwork's TOS (They never bothered to read Upwork's TOS.). In my expereience, the client will typically back down and accept just going with Upworks TOS.
If the client still insists upon their own contract, I would be very wary. I had one potential client do that with me. The contract would have been, legally speaking, binding and a total nightmare for me. That particular client also made false claims on his websites, etc. Very shady fellow in my opinion. I reported him to all applicable authorities.
Bottom line: If you do decide to sign any outside contracts, have them reviewed by a lawyer first. Some can be fine. Some can be the ruin of a contractor.