The more important characteristic to understand about European Walnuts is that are grown in much more humid climates than where American Walnut typically is grown.( The same has to be said for walnut grown in S. America, or in Asia.) In spite of kiln drying, it is likely to develop checks, and small cracks around inletting on a stock- the rear of the tang is common-when the gunstock is stored indoors in a dry room of a house during the winter. If you see a crack developing, relieve some wood with a fine chisel, and put a lttle stock finishing oil back on the spot. If the crack is long enough when you find it, or wide enough, you may want to use a glue, epoxy, or some combination of filler and epoxy to seal the crack to keep it from enlarging.
This kind of checking can happen even on American woods, and does, because our houses are so dry during the winter months with the artificial heating we grow accustomed to enjoying. In the North, the relative humidity is so dry, it doesn't matter whether your house is warm or not- it is too dry for these walnut stocks, and over time- maybe not the first year- you are likely to see a split or crack develop. The only way to protect the guns is to humidify the air artificially, and as of now, I know of no humidifier that has sophisticated enough controls to allow you to humidify a gun case to protect the stocks, without contributing to the rusting of the gun metals.
The only hint I can give is to not exhaust the steam from your shower in the winter, but open the door of the bathroom and let the steam out into the house. You can also leave a pan of water in the oven over night, and let the evaporating water fill the house. But, oil and check your guns every week if you try this, whether they get used or not.