I know the question is a few days old, but for a few months I had a lot of success doing OHP three times a week with no bench;
Monday: volume - 5 sets, started at 5x5, increased weight when I got to 5x8
Wednesday: 2 or 3 sets of 5, nowhere near failure. Weight was whatever I felt like. Sometimes I used dumbbells.
Friday: Work up to a heavy set. Single at first, increase the weight when I could do 4 good reps.
After 3 months of that I switched to lifting 2 days a week, so I shifted Monday's session to Tuesday, eliminated Wednesday and kept Friday as it was. Been doing that about five months now and I'm still seeing good progress.
Either of those templates might work with bench instead of overhead?