This is the first time i have heard about stabilising the hands. I can't make the connection, what would that do if you have CTS? if the muscle starts swelling it will compress the nerve and the nerve is already compressed due to the bone structure.
Gyroscopes are just straight up torture devices for me, as in, 10 seconds and i am out ;)
https://frictionlabs.com/blog/taping-fingers-in-rock-climbin...
But ask your doctor how to stabilize your hand optimally.
And again start slow no weight on the hands, it's about moving them, not overload them (at least in the first 3 month..or more)
Oh and Gyroscopes are extremely good for warmup and for breaks at work.
And no painkillers when you do climbing/boulders.