A great practical question.
A clip will do. Most any Snark will get you within 90% of what you need. This alleviates the need for a 2-channel tuner, which is absurd, but what Chapman Stick players require. Know your battery type and buy them five at a time. Leave one in your glove box and one in your gig bag.
I have a Peterson Stroboclip which has stays with me, even if I have pedal solution for tuning. I use this for all kinds of guitars, basses, mandolins and Chapman Sticks. A clip-on doesn't mute though...
If you were using a small mixer that had an effects send, you could use this to great effect in that both sides of the instrument could access a mono tuner via the send. Adding a 2-channel mute at the end of the chain allows one to mute and tune both sides in a performance setting.
For those using the TRS Output on their SP-2 Preamp, you can take the mono out from here to your tuner. The only snag here is that you need a 2-channel mute that is downstream of the preamp. This is for free. The tuner stays on the whole time allowing me to check my tuning at performance time. I may have picked this up from Rod Serrao.
The Source Audio EQ2 supports dual signal processing and has a built in Mute / Tuner - alas, it can work on one channel at a time.
With my single box Stompmix-4 setup, I am back to the Petersen as I can mute both sides from the Stompmix-4.
The Petersen Stroboclip is my musical
Patronus lol. I keep my eyes on it like I keep my eyes on my coffee.
There's a fun FHF vid on tuners for Chapman Sticks up on YT somewhere.