Caro-Kann Pronunciation

My guess is /kɑːɹ̠əʉ̯.kæn/ (car-ough can).
BTW, people providing answers to this question can you please give it in IPA also, as topics about pronounciation get very confusing when everyone is using their own ways of transcribing text.

There is apparently question about the second word as well. I have always thought it was one of the following:
Care - o - con
Car - o - con
Like a con man, not a tin can.

I've always called it car-o-con which probably isn't correct.
I suspect that Caro is properly Care'o.
Kann is German and is pronounced(unless the name is different from the common word): https://forvo.com/word/kann/
I don't think English has that exact vowel sound which to my ear sounds like something intermediate between the vowel sounds of can and gun.