Cast iron or stainless woks are perfectly fine but high carbon wok is not really practical to be used in a charcoal kettle.
Why? Just curious.
Sent from my iPhone using Weber Kettle Club mobile app
You don't get much temperature control when using charcoal. High carbon requires you to continually cycle from low to very temp in an instant, which can't be easily done using charcoal. Only workaround is to lift the wok in and out or away from the heat source. In this case, you'll need a smaller wok with a long handle. In general this applies to stir frying in which a high carbon is unmatched. Sure you can use it for frying, braising, boiling etc and don't necessarily have to constantly fiddle with temperature but there are much better options for those types of cooks.
Also a propane burner will reach higher temperatures than charcoal. You can definitely increase the temperature of lit coals but you'll have to stoke it or add wood splits/logs.
Been using a high carbon wok for over 30 years and was never satisfied with the results using a kettle as a heat source. Ended up installing a gas burner on one of my kettle.