First, I guess I'd have to figure out if I'm running remotely and second I'd have to figure out whether my remote connection is a standalone remote app or an app running on a terminal server (that may be tricky).
But, once I've figured out all those awful things, is there a way to run a windows function like ShellExecute locally instead of remotely?
The reason I'd want to do this is because I launch a web browser to view rather high bandwidth things that require javascript and flash and certain sysadmins who administer our product aren't too keen on having to make unnecessary and insecure modifications to their terminal server farm.
Yes, if the clients are running Windows and you can install software on them.
See Remote Desktop Services Virtual Channels in MSDN.