I am looking for a beanie like this one from OR but without the fleece liner.

I want something that will stop the wind but without any insulation.

I did a google search and came up with some stuff but when I looked at the same product in multiple places the descriptions left me unsure as to whether it had insulation or not.

Does anyone have what I am looking for?

I used to have one of the windpro hats and they are the tits. But they are fleece like you said (I'm bald and need insulation).

OR used to have a windproof had that has thin fleece, but I don't see it on their website. I have one of those but can't remember the name.

You could just go for a windbloc ear band to cover the ears. I have one by North Face (they call it windwall or something). Wear it with a baseball cap and it would do what you want.

Wife and kids have been using some neck gaiters that can be used as a beanie.

Would a spandex beanie be wind proof?

Windroof?  No.  But, probably good enough for what you are after.