It might not be the most elegant way of running Windows applications in a non-Windows environment, but if you're don’t mind trying exotic solutions, then thin client software company 2X might have something for you.
Their 2X application server linux client allows Linux-based PC to communicate with the 2X ApplicationServer for Windows Terminal Services.
Obviously, it means that you should have a Windows-based server housing the applications as well since the Linux clients are actually running the applications from the server rather than on the clients themselves.
Working in a way similar to Windows Own Remote Desktop, it saves not only the cost of the Windows License, but it is also easier to maintain and to control.
The Application Server is free for up to five applications and is the ideal path if you want to use legacy Windows solutions and/or if other emulators like Wine do not suit you.