I'm sure you've thought of this by now, but Wine might be a solution. I can't say I've tried it. C2 doesn't seem to be running anything that Wine couldn't handle. I could see have to run it via the Steam app an issue though. Worst comes to worse, it would only take a few minutes to try it and find out. I think a quick Google search regarding running Steam in Wine would be your best bet. I think it would boil down to that.
With that said, and as you've mentioned, if all else fails then run it in a VM. It would take a bit longer. Setting up Virtual Box with a copy of Windows 7 is a breeze though and that should run it great.
I think the biggest issue would come down to previewing the game. You might end up having to export the game every time and run it naively in Linux to get the best performance to test your product. I could see potential issues with Wine with that. Also using preview in a VM should work but it would be slower than native (Web GL stuff and all).