One essential module for ANY external instrument has to be an input preamp WITH an envelope follower. That last part is essential; given the peculiar envelope that a shamisen has, it's something you'll 100% want to work with for modulating filters, VCAs and the like. That way, you can also use the shamisen as a controller that can be used to impose its envelope behavior onto the electronic signals.
And it's also not expensive; the Doepfer A-119 is pretty much the "gold standard" at only $99, and it provides a comparator gate in addition to the preamp and envelope follower. When the incoming level exceeds your threshold setting, the A-119 fires off a gate, which stops when the level goes back below the threshold.