All three of those are unsuitable due to Omega 6 content. Coconut oil and Olive oil are perfectly fine for frying mushrooms slowly in a pan at medium or low heat.

You're worried about hitting the smoke point, which would impart foul taste to the food, but its unlikely to happen with any competent cook.

Also it's worth noting that the smoke point is different for extra-virgin versus other olive oils. A purified olive oil has a much higher smoke point and can be used for higher-temperature pan-frying. EVOO can be used for pan frying or baking but you have to control the temperature and keep it below about 375. Below that is actually a good temperature for frying mushrooms in my opinion.

And a little bit of smoke with olive oil is fine, the white "smoke" is likely just water boiling out.

That's a very common misconception and a stubborn myth: https://youtu.be/l_aFHrzSBrM

I fry mushrooms (and many other things) in olive oil all the time. It works great, tastes great and as long as you use extra virgin oil, doesn't create any more harmful substances than using rapeseed or sunflower seed oil, probably a lot fewer actually.

You can even deep fry in it, which some celebrated chefs do.