I would be very surprised if a .desktop file is handled by your shell. You'd be better off hardcoding the full path in the Exec directive.
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I found the GNOME Desktop Entry Specification which says:
> The Exec key must contain a command line. A command line consists of an executable program optionally followed by one or more arguments. **The executable program can either be specified with its full path or with the name of the executable only. If no full path is provided the executable is looked up in the $PATH environment variable used by the desktop environment.**