Making soap is a hands-on type of endeavor as far as I'm concerned. Perhaps less so for the large manufacturer that has huge batch sizes and huger equipment. But to want to make soap without being hands-on seems a bit counter-intuitive to me.
Before hand held mixers (that we call stick blenders), soapers used to hand stir with a wooden stick or some sort of spoon. In fact, many still do.
I suppose you could invest in a paint agitator like they use to mix paints at the paint store, but that hardly seems worth it to me.