You can obviously package your moisture-sensitive sealant in glass or metal cans or tubes, which will totally prevent moisture ingress. Aluminum tubes are widely used for this type of product, as long as you have good crimps.
You can also use plastic containers. If you can handle a rigid cartridge container, then heavy-walled polyethylene containers will give suitable shelf lives for most products. If a thinner walled flexible container is better, it may be necessary to coat your plastic with a material with very low moisture vapor transmission rates, such as polyvinylidene chloride.
An alternative is to use multilayer film or sheet materials to construct your package. These types of films are widely used in the food packaging industry.
Many companies have a history of shelf life testing, but one of the simplest ways to estimate the shelf life of your product is to calculate the vapor pressure of water under both your test conditions and the ambient conditions where it will be stored. For example, if you find that your product is still within specifications after 1 week at 85°C and 100% relative humidity (RH), the vapor pressure of water under these conditions is 433.6 mm (from tables in any good materials handbook).
You can calculate the vapor pressure of water under ambient conditions by first checking weather tables for any particular location in the world. For example, if average conditions at a location are 20°C and 50% relative humidity, the average vapor pressure of water under these conditions is 17.535 mm (from tables) x 0.5 (50% RH) = 8.76. If you divide the vapor pressure under your test conditions by the value at the location, this should allow you to estimate the shelf life. In our example here:
Shelf life = 433.6/8.76 = 49.5 weeks