You want Flash Player "Standalone"
See official Adobe webpage http://www.adobe.com/support/flashplayer/downloads.html
You want the last download in the list for your operating system. I.E: the Windows version is listed as Download the Windows Flash Player 10.3 Projector (EXE, 5.51MB)
Now, Flash Standalone doesn't install, you must place a copy in a directory that will not be deleted. I personally place a copy in my Program Files>Adobe (folder).
You "can" make Flash Standalone the "default" Flash player by Right Clicking on a .swf file and choosing
Properties>Opens With: (Change)>Browse to the location of Flash Standalone (I.E: Within Program Files>Adobe) and selecting the Flash.exe file>Click OK>Apply/OK.
ActiveX versions are "browser" plug-ins. The browser (Internet Explorer, Firefox, Opera, Safari etc) shouldn't be your default Flash player. That's like having all your image formats default opening with a browser! It's hardly to the best way to preview your .jpg's and the same with .swf
All that said, the .exe file is just that, a fully functioning executable file. You should NOT need any form of Flash installed. The Flash player should extract to a temporary directory so you can display the Flash content.
Just like building a "Projector" file using Flash Standalone. Where you take a self contained .swf file (Tourweaver can produce these) and you open it with Flash Standalone and then go to File>Create Projector
This makes a copy of the .swf file and combines it with the Flash Player to make an self contained .exe file.