I'm using the most recent version of Kubuntu, and i've created a shortcut on the desktop to point to a *.sh script i've written to synchronize files between locations. The script works in a snap through the shell, but when i use the shortcut, KDE tries to create a new window for it. This window just hangs in the taskbar, and the Konsole icon blobs around my cursor until the operation seemingly times out with the window disappearing about 30 seconds later.

I'd rather have a more Windows style shortcut, where it either removes the window upon completion of the script, or it doesn't create a window in the first place. Is there a way to do this?

Assuming that you've created a .desktop file ("Link to Application"): right click on the file -> Properties -> Application -> Advanced Options. Either check "Run in terminal" or uncheck "Enable launch feedback".