Can I completely cancel the effects of using a smaller batch size by reducing the learning rate?
Are you aware of this article/tutorial?

https://machinelearningmastery.com/how-to-control-the-speed-and-stability-of-training-neural-networks-with-gradient-descent-batch-size/

I did not study for this answer, but I would guess that when you assure that the batches are randomized, a smaller learning would give the same result.

My guess would be that you divide the learning rate by the square root of the batch size reduction factor.