As of the time of me writing this answer, there are no ways to tell Steam to open Windows games using Wine. Many people have asked, and want this feature.
The only workaround to getting Windows games running in Linux (under Wine) is to run Steam itself inside of Wine. I can understand why this is problematic, but this is the way it was designed.
Additionally, Valve has released a response as to why they won't be adding this in as a feature:
WINE is definitely a useful tool for some things, but we're taking what we think is a more sustainable position by asking game developers to support Linux and SteamOS natively, for current and future titles. We think this is mostly what gamers want, too. It puts more power into the hands of developers and will result in better quality games in the end.
In short, there's nothing you can do beyond what you're already doing.
With the release of the Steam Machines, VR systems, and Vulkan, Linux gaming might finally begin to rise -- if we have the games. You can always try to contact developers of games and nicely ask for Linux support. If enough people show interest to justify the extra work, more developers might be willing to put the effort and energy into making Linux compatibility a thing (looking at you, Bethesda).