What you are suggesting is a good start - but hits one major obstacle... windows is specifically designed
not to run from a USB attached drive.
What you could do is Migrate the system. (move the working system using special software), don't worry, it's quite simple, more so on a desktop than a laptop
Take a look at this video ...
View: https://www.youtube.com/watch?v=eKIRvH7jwx8
I will advise to backup all your valuable content for safety (this type of transfer although very safe can very rarely cause corruption), and at a later time consider moving this to the old drive away from the operating system (or easier still delete the old version of the OS leaving the data in place. This would allow you to update your system without risking damage to your data
I would also suggest that you install the SSD into the first Drive connector on the motherboard
after it's all installed as this will allow the system to be the default if something ever happens
There are many different software packages to perform the migration, take a look at Macrium Reflect, Aomei partition software, Minitool Partition Wizard, all of which are available in free versions that are good enough for this job