While it is true that water is very effective at getting everywhere, there are two key concepts to keep in mind. Permeation rate and duration. Permeation rate has two components-leakage and diffusion. Leakage is straight gas transfer, and with thought, care, gaskets and seals can be completely eliminated. Diffusion is much slower, but basically impossible to stop, though proper material selection and physical geometry can reduce the rate dramatically. Putting desiccant in the protected volume you can keep the humidity below the dew point for some period of time.
Doing this analytically is possible in principal and is done routinely for some equipment configurations, but is difficult and has significant error bars. It involves estimating the moisture content of items inside the protected volume, all leaks and area, thickness and diffusion rates for all diffusion paths, and moisture capacity of the desiccant all as functions of time, temperature and pressure
It is more practical to take an empirical approach. Make your chamber as tight as you can, put some desiccant in the chamber and monitor humidity over time (admittedly this part is tough if you are talking about very low temperature). Be sure to include a pieces of gear similar to your precious to simulate that moisture source. You can adjust desiccant quantity and sealing effort based on your results.
You can also help the problem by dehumidifying the air around the chamber, or doing a dry nitrogen purge of the chamber. In many cases a purge is achieved using the boil off from the LN2 used to cool the chamber, but high pressure bottles of dry nitrogen are not horribly expensive.