You can't really just spawn off 'part' of the Windows install. In this case, just the OS.
If you think about it, everything installed on that drive becomes part of the OS. Applications that live in Program Files, information that lives in <User>/AppData, everywhere in the Registry...
So, to proceed:
From the HDD, move any files OUT of your User libraries (Documents, Pictures, Videos..). Just make a general folder or two somewhere for these.
Unhook the HDD
Install Windows on the SDD
Change the boot order to favor the SDD (now the C drive)
Install any applications you want on the SDD
Reconnect the HDD
Now you can begin the task of putting things where you want.. Videos on the HDD (in a different folder)...