Litigating this is like arguing about whether George W. Bush was a southerner. He was a Connecticut blueblood who grew up in the South, made his political career there, spoke with a southern accent, married a southerner, and so on.
The war with Ukraine has made questions of Russian and Ukrainian ethnicity much more salient then they used to be, but it's important not to project that onto the past. The situation with Khrushchev and Brezhnev is a lot like W's—they grew up and made their political careers in Ukraine; Khrushchev in particular had a strong southern accent.
Аnd if you absolutely insist on blood tests, then you'd have to count Gorbachev as half Ukrainian, which would be a further bit of proof about the effectiveness of assimilatory policy...
Khrushchev in particular had a strong southern accent.
You can take the matter up with his granddaughter if you like:
I remember my grandmother saying that Khrushchev spoke Ukrainian all the time and that it was so embarrassing because it wasn’t the real thing! That said, Khrushchev was a Russian. It’s erroneous to say that he was Ukrainian—as Henry Kissinger just did, in a recent article. He did not transfer Crimea to Ukraine because he was Ukrainian. He was a Russian.
That's a very odd adjective choice to apply to the Georgian one.
The other 3 are usually cited as Khrushchev, Brezhnev and Chernenko, but the former two were of Russian ancestry.
That leaves us with Stalin and Chernenko in our multicultural icon set. The latter having of course served but a year, mostly as a walking corpse.