I haven't followed the GS Mini line much, so I don't know off-hand whether a no-electronics version of, say, the GS Mini Koa is currently available; check the Taylor web site. Not so many years ago (3-4 to be exact), the GS Mini line came standard without any electronics, and Taylor offered an extra-price, drop-in component called ES-Go to provide an acoustic pick-up for the GS Mini.
If none are available sans the electronics in the currently line-up, you can try looking for a GS Mini that's 3-4 years old; about that time the standard body laminate was Sapele, but there were a couple of limited editions that came out with different laminates and no onboard electronics: Blackwood, Maple, and Rosewood (2012 Spring Limiteds); and Koa and Rosewood (Fall 2013).