Possible to launch non-steam games, with the overlay, via a non-steam shortcut?

So, here's the deal:

• I have quite a few non-steam games, which I usually launch via shortcuts in a folder.
• I've added these to Steam before, but they regularly disappear, and it's more hassle than it's worth.
• However, I'd appreciate being able to use the overlay for time / chatting / etc.

Any ideas?