If you right-click on the Klipper tray icon, select “Configure…” and then “Shortcuts”, you can assign shortcuts to move back and forth in the kill ring, and to paste. I have assigned S-v for backwards and S-C-v for forward. Then the usual C-v will paste. The tray icon also shows you the current selection (and the ones above and below) in the killring, as you move through it.