There have been a few threads bemoaning the difficulty in getting dwarves to use high-quality equipment, even when it is available.
I think the most logical solution to this problem is to introduce a new appointed noble, the Supply Officer (or some such name), whose job is to oversee the allocation of equipment to the military. They would use the Appraiser skill to judge good equipment, the Record Keeper skill to keep track of it, and the Organizer skill to ensure that each dwarf has good up-to-date equipment, with the best stuff going to the most highly-skilled dwarves. They might also have an associated screen where the player can make choices about how equipment is distributed (telling dwarves to use whatever is available rather than the best stuff, say, or prioritizing different things -- carried weight verses equipment effectiveness, say.)
The Drill Instructor would be a similar appointed noble who oversees military training. One of their primary roles would be to ensure that dwarves use weak weapons for training rather than just grabbing whatever's on hand -- a higher management skill helps with this. Their management skill might reduce sparring accidents in general. They would also use their Intimidator skill to improve military training when they're present (they'd wander into the barracks and yell at dwarves while they train, or whatever.)
Together, these dwarves would hopefully provide a realistic way to improve the way dwarves use available equipment.