The latest version of Corel PaintShop is compatible with Windows 10 and previous versions of Windows, but it's impossible to say if this one from 2010 will run properly on Windows 10.
Firstly, launch it as it is and check its behavior. If you have issues, then right click it and choose Properties > Compatibility. Select a previous version from the list, and then launch the software with the Windows XP or Windows 7 tweaks.
Compatibility information for latest version: Windows 10, Windows 8/8.1, Windows 7 with latest service pack (32-bit or 64-bit editions);