I am assuming that you can’t reach the wound.
Before you remove the old bandage1, find a door frame or some other vertical outward corner. Mark the height of your wound by gently(!) leaning on it - even if you can’t reach the actual wound, you should be able to reach back far enough to determine the height with reasonable precision, add some kind of removable marker. Also, if your wound is slightly off-center, note where the vertical edge touches your back. No need to hurry, take your time.
To clean your wound, you can use a towel as an “extended washcloth”: Wet the center and gently maneuver it across the wound or, if that’s too harsh, flip it over your shoulder so that the wet part meets the wound and gently lean on a waterproof surface. Think “dabbing with your body” instead of dabbing with the cloth.
Don’t fiddle with anything to apply the ointment separately, putting the vaseline on your band-aid will get it to the right place automatically.
And now on to the band-aid: Prepare a generously sized piece (if it’s a bit bigger, it won’t matter if your not as precise in positioning it). Add the ointment on the padding of the band-aid and remove the paper from the glue strips. Go back to your door frame and fix the band-aid with a loop of tape (I recommend washi tape), sticky side outward. Use your mark to get the correct height and let the edge of the door frame meet the center of the band-aid. Like this:
Lean on the band-aid (remember the correct vertical position determined before!) and use the edge of the frame to push the sticky parts onto your skin. The tape used for mounting the band-aid should stick more to the smooth surface of the door frame than to the fabric of the band-aid, especially if you used washi tape.
Side note: The method works, I successfully tried it myself.
1 Will there be a second question ”How to get a band-aid off a wound I can’t reach?”...