Do asexuals also get nervous and uncontrollably and awkwardly smile when they cross paths with someone that they consider attractive?

They can, it really depends. Asexuals can get nervous around crushes or just people they find attractive. It just depends on the person, asexual is a veeery broad spectrum and it's you who gets to chose if that label identifies you, nobody else has to validate if the term suits you.

I do but I also am also autistic. So I'm awkward around everyone regardless.

Personally, only because of social stigma.

I worry that paying attention/compliment to someone being aesthetically good looking will be taken as a sxual interest when it isn’t. I’m as sxually interested in them as I am a cute cat or a pretty flower, which I also smile at seeing.

So I’m a bit more hesitant to smile at the pretty human than I am smiling at the pretty kitty or pretty flower.

I personally don't but I would get awkward if someone was attracted to me