Well, I guessing Connections does not show as an update because it requires at least WP 4.1 now… If you can not update WP, then, you can not update to a version of Connections which has the CSV export features. Sorry, but there is really no way around that.
The only option I can think of is to duplicate the site using maybe DesktopServer. Then update WordPress on that duplicate so you can update Connections, then you can use the CSV export.
Probably not the answer you wanted to hear, but I hope it helps!