To quote Shelly, "ugh, that's ugly".
With a quick web-search, though, I discovered something. Since the Flash format and player source are both open, a few folks have released much-improved executable-makers for Flash. I've tried four of 'em and have found two that are really good. Both work similarly --you get a wizard-style interface in which you give it the location of your SWF file along with a buncha options (icon, window-size, etc). It then generates a .exe file for you.
First is Flashnpack. With just a quick look, it appears to be the more capable of the two. You can set frames that are triggered when you right-click, so you can make custom right-click menus and such. The other might be able to do this, but it wasn't as obvious. It's $89.
The other is Flash Studio Pro, which seems like a rather lofty name for a projector-maker. Both claim to give you a bunch more Flash commands to do stuff like save to the registry and such, so it might be more capable for all I know. Nicest thing about this one is that it claims to be free for non-commercial use. Since I'm doing a non-commercial project, this is a considerable advantage, but I still haven't gotten my serial number yet. For commercial use, it's $59.99 for the standard version and $99.99 for the pro.
The other difference I saw was executable size. Even with Flash Studio's best-n-slowest compression turned on (which was indeed slow), my project ended up as a 1.12 meg executable. The Flashnpack executable came out at 635k, which is a pretty considerable savings. Both played just fine, and I couldn't tell the difference between the two. Taking first impressions into account, I'd probably go with Flashnpack.
As to the project I'm using this for, it looks like it'll officially be unveiled on the 22nd. Of course, if you frequent the gamedev chat-room, you've probably already seen it. You'll like it.