Who's said anything about removing the current population? A change in the sovereign power (the US for Denmark) yes, but the current residents would remain with their property holdings intact. Much the same way property owners kept their titles in the Virgin Islands and New Orleans with the Louisiana Purchase.
that is the only way to move the population. Either ship them back to mainland or sell them off together with the rock.
I find ignorance here by some reminding us that it happened in the past. Yes, we are not 100 years ago so just because it happened does not mean it will or can happen