It sounds like the problem with your (standing) overhead press is either form or maximal isometric strength in the core. Changing to an exercise that removes both of these factors and doesn't improve them does not seem like a productive way to increase your overhead press.
Without a lot more details on your training history (sets, reps, loads, frequency), it's difficult to know how to fix this. Maybe increased volume or frequency with the lift will help. Maybe your shoulder mobility is such that getting into proper overhead position is difficult enough that your lower back position gets mangled, and so you should work on your overhead mobility with wall slides, Hindu push-ups, handstands, and more diligent shoulder warm-ups. Maybe you need to deload. Maybe you need to do more supplemental lower-back and abdominal work. It's tough to know without a detailed log of your training as well as a form check video.
So yes, you could replace the (standing) overhead press with the seated overhead press. It just won't help your standing overhead press.