I think this should be something that the player has an option of doing, but is not pushed into, and that the captain of the guard is the wrong choice of instructor. Maybe an (o)rders (civilians train and civilians arm).
Civilian (t)rain means that a new noble position of trainer is opened up. trainer can overlap with any military or non-military noble position, but is more or less full time for large forts. options are never, optional, mandated, available. Optional provides free classes to whoever care to come for a good thought and some new skills, mandated cycles everyone, whether they like it or not, complete with associated bad thoughts, and provided opens government classes that need to be paid for (once the economy is back, naturally).
Civilian arm (w) can be set to none, mandated, optional, or private. Mandated requires everyone or all appointed individuals to carry whatever arms and armour you say they should (bad thoughts), optional lets you put unused military supplies in a stack, and anyone who feels the need can go take what they like, and private lets you open a military supply store for individuals to buy from.
Government subsidies can be put in place to make steel and training little more realistic for the common underpaid dwarf.
Edit for formating