an alternate version of a gene being from the same geographically-linked pool is totally dependent on how geographically-diverse the parents' genetics are to begin with.
I don't know your particular family, but if, for a hypothetical example, a mom is 100% Danish and Dad is 100% Japanese (this wouldn't be the case, but just for concept) if you don't get the danish gene you are very likely to be getting a Japanese one.
So yeah, it's for sure a "your genes may vary" situation.