Stop that bullshit. Be frank, and say that compensations will be different because the market is different. That's it.
'Cost of living' is bullshit without specifying what 'living' means. That needs you to specify what your employees should be spending their income on. If an Ukrainian employee spends all they income on buying houses and going to restaurants and hairdressers, then their cost of living is really way cheaper than someone living in, say, London and buying similar houses and eating in similar restaurants. However, if our imaginary Ukrainian employee wants to buy cars, gadgets or wants access to high-quality healthcare, then suddenly the cost of living is _higher_ for them than for someone living in London.
So screw the bullshit around 'cost of living'. Do whatever you prefer about compensation, but be straight about it.
(The article is not great, though, e.g. stuff like "Whatever one's situation is, however difficult a negotiation might be, treat people like they were your friends" -- well, no, your colleagues are not your friends; some of them might be, but you better have friends as your direct reports.)