Hello @lethalz
You can install that SSD in place of the old HDD but you will also need an adapter like this since the old HDD is 3.5 inch and the SSD is only 2.5 inch. https://www.amazon.com/Valuegist-Internal-Mounting-Bracket-Adapter/
If you are only removing the old HDD, no data on that drive will be erased obviously. You stated you backed up everything you needed to an external drive anyway so you are covered.
Here is the manual that gives a vague look with pictures on how to access the drive. Scroll to page 13... http://h10032.www1.hp.com/ctg/Manual/c05933340.pdf
You have two options on clean installing Windows to the new SSD from scratch (so to speak).
- You have the Microsoft OS direct from them without the HP stuff... Create media Windows 10 and an 8 up to 32GB USB pen drive can be used. If you do not use a microsoft account to sign in with, simply disconnect the internet first, then install windows. It will give you an option to create a Local Acct.
- Or you can use the HP Cloud Recovery tool. 32GB pen drive required. HP Cloud Recovery Tool (how to use)
You do not need to know your activation key now days. Windows will auto activate once its connected to the internet.
Let me know what else I can help with.