There is absolutely literally 0 reasons to ONLY want the Home & Business version of Office.
All that means is that you don't get all of the office suite applications. If you are doing that to save space: when installing the full Office Professional Suite, you can deselect the office products you never use to save space.
DVDR_Dog mentioned this already.
And no: even in a "business environment", installing the Business & Home version DOESNT EVEN HAVE that branding ANYWHERE on the system anymore.
Microsoft stopped using branding on its products I think around when Windows 8 was being released and it was all more tablet like. They just call the apps by their names now: Word, excel, etc.
So just use RevoUninstaller to uninstall your current version of Office, download a Office Professional Suite so you can then finally deselect any of the apps you don't want, and then can activate using KMSPico, KMS Auto Net, Microsoft Toolkit, etc.
You already mentioned that you do NOT have a legal key. So the activation method does NOT matter, as long as you have the proper installation in the first place.
When it comes to Piracy: you don't really get to say "I only want to do it this way", that's why you pay for things: so they can be YOUR way.
I'll DM you the office professional torrent I use, and it comes with an activator.