STR from the v8.6.3 (there are probably other such dialogs to invoke):

• launch empty N++, make the "new 1" tab dirty by typing something
• set Backup settings ON like:
  
• have the minimizing to systray ON (Settings > Preferences... > MISC. > Minimize to system tray)
• close N++
• relaunch N++
• goto the N++ .\backup\ dir & delete there the "new 1" backup ("new 1@YYYY-MM-DD_HHMMSS" file)
• minimize N++ (to systray)
• right-click on the N++ tray-icon & chose "Close Tray Icon" from the popup
• click on the Cancel in the invoked dlg:
  
• now you will have the N++ process running but without any GUI visible (no systray icon either)