Not entirely sure how well this works but as you've only broken the wrist and finger you can still use your elbow to hold the diaper in place.
I change standing up, so I would use my left hand to hold it open against the wall, position it correctly against my back and lean into it.
Then draw it up, use my right elbow to catch the top and hold it against my waist, then you can just roughly stick the left side bottom tape down.
Now you've got a tension point to pull against for the right side so you can do that up tightly, then you can retape the left and do the same with the top.
Voila, you're somewhat reasonably taped in.