man, this is not something I would do. Firstly, cast iron is brittle. I'd be afraid of weakening with a hole anywhere. Secondly, I'd be afraid of any residue from the penetrant upon re-installation. Tapered metal on metal must be clean (think drill press or milling machine chucks)

The key should only be a safety precaution. if the drum slips, it will make the key hourglass shaped, and spread the slots in both the drum and the axle, effectively ruining both.

I expect the small hole is okay. But man, be sure to clean the tapered surfaces very thoroughly before reassembly.

The puller you have sounds like the right tool, and it will work without penetrating lube. It might not be easy. I've beat on those things for hours, to no avail, left them under tension overnight... only to be awakened by what sounded like a gunshot at two in the morning, likely due to temperature change.
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-Matt I ♥ my ♂