Yes, it should be possible to get Skyline to run on another computer as you describe.
Skyline usually gets installed in the user's home directory by the web installer.
You might find it easier if Skyline gets installed in the C:\Program Files folder, in which case you should use the "Skyline Administrator Install":
https://skyline.ms/wiki/home/software/Skyline/page.view?name=install-administator-64
The conventional way to drive Skyline is by writing a Windows batch file which invokes SkylineRunner.exe (if you don't know where Skyline is installed) or SkylineCmd.exe (if you know which folder Skyline is installed in).
You might want to use Skyline Batch instead of writing a batch file:
https://skyline.ms/wiki/home/software/Skyline/page.view?name=skyline-batch
The place to get the most up-to-date documentation about the Skyline command line interface is with the menu item "Help > Documentation > Command Line". (Actually, I guess "SkylineCmd.exe --help" is a different way to see the same information).
Let us know if you run into any problems.
-- Nick