Bending insensitive connection or highly flexible/thin cable
Lavelier microphone cable sounds like what you want, it is the cable normally used between the head and transmitter pack on bodyworn radio systems used in live performance. 

Usually it has two cores plus an overall screen, it is highly flexible and reasonably robust, but can be a bit of a swine to terminate. 

Here https://www.canford.co.uk/MOGAMI-LAVALIER-MIC-CABLE is a 2.5mm od variety, you can probably find smaller variants.  

And here https://www.hhb.co.uk/product/mogami-miniature-balanced-lavalier-microphone-cable-(2901)/2379/ is a 2.16mm variant.