Well, obviously, you have an OS on both drives. You must have an OS on the new HD or else you could not simply discconnect your master/original drive and boot from the new drive. And, by the way, you did say this but you must also be changing your second drive from slave to master when you do this. Right?
What OS do you have installed on both drives? Have you thought about setting up a dual-boot configuration? That would allow you to choose which drive to boot from during startup and eliminate the need to physically disconnect a drive and change master/slave settings. Or, since you have an OS installed on the new drive, why not just make it your master drive and the old drive the slave?
As far as your original question about running CS, I'm under the impression some games can be run by merely clicking on the .exe file. In other words, they do not have to be "installed" under a conventional install procedure that creates entries in Windows Registry. Is that right?
I'm not a gamer, but I have a friend who once ran a game on my computer in this manner, if I recall correctly. I surmise this is the premise behind your question. Is that right? I'm not familiar enough about CS to give you an answer.
