The reason I want to change the lamp-cord to a shielded, high quality cord is to both give the TT cleaner power and to prevent emi from leaking out of the cord into the myriad of signal carriers that surround it.
What you describe above would not ground your TT. It would shield the PC...
In this case the shield of the PC would connect to the AC plug ground pin only. On the other end of the PC tape it off. TT end just floats....
Grounding the TT would mean connecting the chassis of the TT to the safety equipment ground of the wall receptacle. This could cause an unwanted ground loop hum.