With AIR 2.0 you now can:
if(NativeProcess.isSupported)
{
var file:File = File.desktopDirectory;
file = file.resolvePath("StyleLookupold.exe");
var nativeProcessStartupInfo:NativeProcessStartupInfo = new NativeProcessStartupInfo();
nativeProcessStartupInfo.executable = file;
var process:NativeProcess = new NativeProcess();
process.start(nativeProcessStartupInfo);
}
You also need to add this to your descriptor file.
<supportedProfiles>extendedDesktop</supportedProfiles>