You can actually disconnect the hard drive and install windows then connect the old drive as long as the system knows to boot from the SSD.
You may run into one issue. Permissions.
The new install of Windows may have to take ownership of files on the hard drive.
Can you please let me know how much space you are using?
You can shrink a partition to move files without 3rd party software. 3rd party software is just more easy in some cases. One thing to never do is move the system reserved partition or the start of c: as that can prevent proper startup of the system. Shrinking the c: from the right side does not cause issues and just allows you to clean off the old crap.
Steam is VERY friendly for copy+paste use(I normally install it then copy the copy with all games over it). It will automatically perform first run tasks on games.
I also DO recommend a larger SSD if you can.
On this system, I have 2 SSD's one for Windows and games(and Windows 10 as well now) the other for more games. They are each 256 gigabytes and I wish I had a bit more space.
I have no hard drive in the system because all my files are on another system access over the network(this means all my systems can share the same personal files and backup is much more central). The system that holds the files is my media center pc and does have a single 128 gigabyte SSD, so it can be done, but I do not have many games on it or anything.
My media center system runs the SSD for windows programs and some games(started life with a single hard drive) a hard drive for all my files(WDC RED since it kind of is used like a NAS) and another hard drive for media center recordings(notebook drive).
Due to your lack of drives, If you want to remove all the old Windows crap, you will have to shrink your partition and move files over. Too many hidden and security restricted files to make it worth trying to manually remove all the files(and you may have a system reserved partition).
You can do this AFTER installed Windows on the SSD.
These images are from a guide for a user that wanted to reinstall and keep files.
1. You would hit Start + R to open RUN
2. Enter diskmgmt.msc
3. Right click the partition you want to shrink and select Shrink
4. Wait a second while it determines how much you can shrink(files in the way prevent this. 3rd party software can move these files and allow you to shrink farther in some cases).
5. Input the size you want to shrink by 1gigabyte is 1024 megabytes
6. and 7. You will now have some unallocated space and can create a new partition(volume) in that space.
You will now have a location to dump files you want to keep when you later remove the Windows partition and system reserved(make sure you get everything you want and do this when running from the SSD).
My Images show c : , but yours will NOT be C : because your SSD will be the drive that has c : . Make sure you only remove partition from the hard drive. It will be easy to tell by the larger size.