Is there such thing as an EMG sensor which doesn't use electrodes?
This is not possible because the electrodes are also capacitors and any loose fitting varies the capacitance from pressure of the electrode. When there is a galvanic charge on your skin electrode interface modulating the capacitance also modulates the voltage.To avoid the skin motion noise from modulating the galvanic charge , I believe the resistance must be much less than the capacitive Impedance change at the surface 

. Thus silver oxide pads are preferred or thin sticky gel.

The impedance of each electrode must low compared to body to air impedance and fairly equal in order for good CM line voltage balanced differential CMRR rejection.  Why ? The body surface acts as a dielectric antenna for stray line voltage. Nothing is absorbed except it interferes with your CMRR of high gain high impedance differential amp or INA.