No matter how you connect the Mobius, it's own DAC (and DSP) is always in the signal path.
There is no direct connection to the drivers if you do use the analog "Aux" input: analog is converted to digital, DSP'ed and then DAC'ed.
There is - to my knowledge - no aftermarket CCK.
Use the original Apple one, cost ssome 35$.
There are two versions, one with additional lightnig power connector and a 2nd one without.
You need to switch off Mobius battery charging if you use the 2nd one: press and hold the volume button until the gypsy muse tells you " Charging off".