You are contradicting yourself. You want to put ONLY the OS on the new SSD but... without deleting everything?!?!?!? Do you want to clone everything AS IS or only have Windows OS installed? You can't do both...
I think what you are trying to say is that you want to keep the current data but move the OS over to the SSD.
Only way to really do this is do a fresh install of Windows on the SSD, install the old hard drive as a spare, copy data off of it to another device, format the old hard drive (to remove windows os off of it) and then copy the data back to it.
You do not want to leave the old drive plugged in and not reformat it. The OS may think you are trying to duel boot and cause problems or try to boot to the old drive first.
Or simple just get an external drive and copy data off into it.