If the powder in the containers still has a bit of a solvent odor, there should be no problem using it. Most smokeless powders made in the last 60 years are very stable compounds, and unless they are stored improperly (high heat, corrosive atmosphere, etc) they will tend to stay stable and usable for many, many years.
Asa for your wife's worries about all that "dangerous gunpowder", no worries. Smokeless powder is a flammable solid, not an explosive. When burned, smokelss powder generates a large amount of gas. As long as the containers have a weak point (which ALL factory containers do), the gas will disapate. On the other hand, IF the powder has been transfered to other containers, such a glass jar, it could generate enough gas pressure to cause the jar to explode. I have seen idiots use glass jars for powder storage, very, very, bad practice! As long as the powders in question are in original containers, you have nothig to worry about.
As DM pointed out, gasoline (particularly gasoline vapor, a real explosive!) is far more dangerous to store than smokless gunpowder.