Right now I would simply add the overhead press work on your bench press day. And the day(s) after your bench day(s) start the workout with isolation deltoid work.
I believe that in your case, right now, devoting a day to overhead pressing might be a mistake. If your shoulders are so weak, they do not need their own day. If anything it could be overkill and actually make them regress.
The delts play a big role in the bench press, so doing isolation work/double stimulation for the delts the day after bench is perfectly fine.
So add 4-5 sets of 4-6 reps on overhead work with your bench workout(s) and do plenty of isolation to start your next day's session. The overhead work doesn't have to be with a barbell. Use the apparatus that allows you to get the best loading without pain.
As your deltoids become stronger and the shoulders healthier, you will be able to benefit from a overhead press day.