Unlike the regular, free version of Skype, Skype for Business is its own animal and you don’t want to try uninstalling it. It’s embedded into a program called Microsoft Lync and companies pay lots of $$$ to install and run this software.
So, no, you don’t want try to install Skype for Business to fix a headset issue. It probably won’t work and it might cause issues in your computer.
What you CAN do, though, is refer to your IT department if your Skype for Business is acting up.