If you install the OS to your boot drive you'll have to reinstall your games anyway, even if you just reinstall them to the hard drive again. "Installing" a program does more than just copy it to the drive, it also configures Windows so that it knows how to run it. When you install a new copy of Windows to the SSD it won't have that configuration and so it won't be able to run the programs on your hard drive.
There isn't any easy way to remove the OS from a drive. It's much simpler to just copy all the data files you want to keep to a new drive and then reformat the one that had the OS on it.
Of course you have a separate backup drive you've been using to keep copy of all your files for safety, right? You can copy all your files to the backup drive and then reformat the drive that had the OS on it. That will be a lot easier in the long run.