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You could mud the bathroom area, but first make sure the plaster is cracked from age alone and not a continual problem. Usually cracked plaster in a 30's vintage home is from age or gentle settling of the property over the last 70 odd years. For what your describing it might be better to float out the entire bathroom with mud then sand.
Make sure you remove any loose material (plaster) from the wall and inside any open cracks before you start floating out the mud.
There would be no need to look for a water proof mud but rather a very good sealer and top coat paint, something like a Zinnzer product (H.D and Lowes sell it) You want a moisture sealer for both priming and the final coats.
I would recommend putting in or getting one put in, an exhaust fan sometime in your budgets time frame.
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