or the fetishisation around mixed race kids, but I
Such a massive issue. I remember in school a lot of white teens saying they wanted mixed kids. It sort of feels like a slight towards darker skin colours and feeds into colourism - they want a ""lighty"" (
) child, not a black child. Totally get why that would feel like fetishisation and offensive.
I think people should leave the compliments to when it's relevant with skin colour. So, as you say, if she had complimented how your skin tone went with the nail polish you had picked (I really do agree with the person who said dusty light pink works super well on me), that would have been fine.
If my Japanese friend has done her hair up fancy, or asks if her hair looks OK, then maybe then would be fine for me to say yes it looks beautiful, it also looks very nourished and silky, but perhaps not OK to just randomly mention it as it could be seen as a fetishisation thing.
Similarly, things like eye shapes can really look very very pretty, but I think should only comment on if someone was perhaps asking about their eye makeup and if it made their eyes look good/enhanced or whatever. Of course you have to use the correct terminology and not be offensive with it, even if you don't mean to be. I think it's called a canthal tilt, where the inside and outside corners of the eye can have a positive, neutral or negative tilt in relation to each other.
There is just such a weight attached to these things as they are usually picked out for stereotyping and prejudice.
I think anything that could be seen as you mentioning something that a group of people have been discriminated against for , even if you mean it positively, needs to be said in the correct context to not seem weird. And don't talk about wanting your kids to have X appearance! I mean that's just a bit weird anyway isn't it.
I'm not sure what exactly you could say in the moment though. 
I'm not very good at that, I always end up thinking of something perfectly sarcastic weeks later!