Stabilization is made in the process of washings with water and sodium carbonate solutions. NG is quite safe in the emulsion with water, as it is after the synthesis and washings. When it separates it is much more dangerous and I wouldn't recommend storing for a prolonged period of time.
Dynamites have lower sensitivity because NG content is low and the ester is absorbed in other solid ingredients. However, it doesn't mean they have a long shelf life, they are meant to be used soon after the production.