Skyline allows you to save a document so that it can be opened by older versions of Skyline.
The menu item to do this is:
File > Share
You usually do not need to be an administrator to install new versions of Skyline, although I do believe you would need administrator access if it was necessary to install a new version of Microsoft's .Net Framework.
If you want to install older versions of Skyline, you can do so from the "Unplugged" installer page:
It sounds like "File > Share" is the menu item you need to use to solve your problem.