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I have been using this wax polish made by Picreator Renaissance Ltd (a UK company) and I am mightily impressed by it. It claims to be used by many museums to protect antique furniture and metal parts as well. It gives a nice hard finish which doesn't finger-mark easily. It's a bit pricey but the company advises it to be used sparingly and my tin, bought many months ago, is still mostly full. Worth a try on your arcade machines and household furniture too.

Usual disclaimer - I have nothing to do with this company and I don't even get free samples.

Not seen that one before. I'm always in pursuit of the perfect silicone-free wax polish. Feedback on its metal protecting prowess is mixed...
I match your "Appointment to Her Majesty" and "Formulated in the British Museum’s Research Laboratory'' with an "Appointment to Her Majesty" (Mylands) and an "As used in National Trust Properties".


Although petroleum-derived, microcrystalline wax is used on various comestible products (e.g. glazing on chewing gum) and is considered food-safe.
This guy has tested carnauba waxes vs microcrystal waxes:



Other brands are available: MW225 Chestnut Products Microcrystalline Wax, Hampshire Sheen Microcrystalline Wax, Sasol Microcrystalline Wax.