Whatever's in the secret sauce, it would still be homogenizing people.
No, that's not how it works. Homogenizing is the absolute worst thing you want to do if your goal is to increase the vigor and adaptability of the species. This is why all the racist eugenics programs of the 19th-20th century failed -- because they were doing it backward. Their bigotry blinded them to the simple biological principle that the vitality of a species depends on a large, diverse gene pool, that a limited and homogeneous one is a recipe for extinction.
And I think you're making the mistaken assumption that the process by which Augment DNA altered Klingon DNA was the same one that was used to create the Augments in the first place. I don't think that's likely. The Klingons used their own genetic engineering methods to inject Augment DNA into Klingon test subjects in order to imbue them with Augment traits, accidentally giving them human cosmetic traits as well. The Augment DNA then jumped to a Levodian flu strain (along, perhaps, with some genes from whatever retrovirus the Klingons would've been using to transmit the Augment genes) and became airborne.
Whatever methods were used to create the Augments in the first place would've been something different, presumbly a germ-line alteration, manipulating the genes of embryos before implantation. Indeed, we saw Arik Soong doing this with the embryos he recovered from Cold Station 12. There's no "secret sauce," there's just coding, essentially -- mixing and matching the genes in the chromosomes of embryonic cells. And the donors for those genes, as well as for the original gametes, would've probably been selected from a variety of different ethnicities, in keeping with what we saw in "Space Seed" and ENT. So any given Augment, Khan included, could be of multiracial parentage and multicultural upbringing. Thus there's no reason one of them couldn't be a Caucasian Sikh with a name that's a hybrid of three different cultures.
So logically a lot of the resultant Augments would be bi- or multiracial.
So why is their leader bleach white? Perhaps the eugenics / augment program got its start in the late 30s?
White is one of the races, so it would be included too. But he's got a Caucasian appearance, a Sikh religious affiliation, a Chinese middle name, a very unusual first name of Central Asian origin, and a Mexican accent (in one version -- perhaps as "Harrison" he adopted a new accent as a disguise). That's a lot of diversity in one package.
(Of course this is an accident. Khan was a product of two unfortunate 1960s TV practices toward Asian cultures -- homogenizing them into a jumbled mass and casting white actors in Asian roles. But fortunately it can be rationalized in a way that fits what we know about the ethnic diversity of Sikhs and that of Khan's people.)
