How does current flow through a mono (TS) guitar cable?
A mono guitar cable (shown lower) has two conductors 

And I quote from here:


  The cable at the bottom of the graphic is a "standard" 1/4" instrument cable. It has two conductors (1 and 2), separated by an isolating ring (i) so that they don't contact each other. The TIP (1) carries the "hot" or positive audio signal; the SLEEVE (2) is the ground or negative audio signal. 




The shield does just that, it shields the inner conductors from noise from stray electric fields (like radios, cellphones and the 60Hz hum from AC Mains) If you want to get a analog voltage waveform 'into your equipment", generate a positive voltage on the (1). Every voltage needs to be referenced from something else to be meaningful, most people use ground or near 0V for a reference. So for the return current or ground in your circuit, connect it with (2)