You don't need to execute the stack. Just use ROP to fill the stack with return addresses that point to "gadgets". Gadgets are basically a single assembly instruction at the end of a function like XOR EAX,EAX and then a RET. Every time a RET is executed the CPU will jump to the next gadget. There are usually enough gadgets inside a program to basically do anything you want.

https://www.exploit-db.com/docs/28479.pdf