The more commonly used thumbcodes can be comfortably signed, by design. There is potential for stress with the less commonly used thumbcodes, particularly those in which the thumb has to reach across to the pinky or down to the base phalanges. Also potentially stressful are the shifted closurs, especially Shift Trio which holds just the middle and ring fingers together.
Stress is greatly reduced by judicious exercise of those degrees of freedom of the hand not constrained by the Thumbcode specification. It is natural for a beginner to picture the closure positions as being realized with a flat hand, with the fingers held straight and lying in a plane. However Thumbcode does not require this, and it is much more comfortable to thumb with the hand held in a relaxed cupped position, allowing the thumb to reach the tip phalanges without needing to stretch. (In this position the author finds Pair the most natural closure.)
Nor is it necessary to separate the fingers sideways. The pinky can be moved away from the ring finger by bringing it closer to the palm as well as sideways; likewise the index finger can be separated from the middle finger by straightening it. (Moving it towards the palm obstructs the thumb's access to the middle finger.)
In general the user should experiment with ways of holding the hand that realize the Thumbcode specifications with the minimum of discomfort. Hand anatomy varies widely, and different people can be expected to come up with different positions that maximize comfort.