Funk means wireless ??

Funk means RF/radio/wireless. The term originates from the first radio transmitter ever, which used spark gaps (spark = Funke, gap = Strecke/Spalte) to generate detectable RF.

So German Funk is actually directly related to the English funk (as in music) etymologically.

Thanks for the detailed explanation.

In this context, yes. More literally, Funk means radio, and the word for wireless would be "drahtlos".

Means "radio".