Built in 1963? There was no International Residential Code back then. Even the CABO One- and Two-Family Dwelling Code didn't exist -- it wasn't created until 1972. This means that unless there was a local (city) code in effect in 1963, there was no code at all. Here's what the 1992 CABO code said:
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View attachment 14713
Bathrooms are not habitable rooms as defined in the CABO code (in fact, bathrooms are specifically excluded from being habitable rooms), so there is no requirement for a heating duct.
Ask the home inspector to cite the code that he/she claims requires a heating duct. The code in effect doesn't count -- it has to be from the code that was in effect when the house was built, or when the bathroom(s) was/were most recently renovated.
My experience with home inspectors is that they too often attempt to justify there existence by reporting as "required by code" a wish list of things that, while nice to have, but which were not required by the code at the time of construction. And that's the only code that matters.