That is also not in question. But Spock said "You should make a very convincing Nazi", not "You should make a very convincing German". Being German is a question of ethnicity, being a Nazi is a question of (political) conviction, a decision that is consciously being made.
The joke was not aimed at ethnicity, but the way that Nazism relied on images, not only physiognomy, but all symbols and aesthetics, to convey ideas. Spock's quip about Kirk was not the only reference to this in this episode: Spock's ears were a running joke of the episode. And those jokes played into the critique of Fascism as a reasonable response to crisis, as it relied on irrational appeals to the more problematic sides of human nature.