If you are absolutely sure that the CD player is inducing the hum in your system and you know a cheater plug resolves the issue, you might want to consider removing the ground plug from your hi-end cable. Of course, it will ruin the resell value of the cable, but it will be a better physical connection than you have with the cheater plug installed.
You might also want to consider retermination the power cord with a plug that is two prong or has a removable ground pin. Or you could always sell the current PC and buy one that is terminated with a two pin plug or has a removable ground pin.
Enjoy,
TIC