This suggestion derives from an experiment I conducted when modding weapons.
When a weapon's skill tag is set to a nonmilitary skill, that weapon is still available for making in a fort, but has no use. It also allows an adventurer to take a nonmilitary skill.
Currently, a special DIGGER tag defines the weapon used for mining, and the AXE skill is hardcoded to be the one used to determine a woodcutting tool.
Why not allow multiple skill assignments per weapon (I might want to test if it already works first though), and let the skill define the weapon (or rather, tool). It will allow a smith to use a special hammer when working, a woodcutter will not use just any axe, but ones specifically marked by a relevant skill, a stoneworker will lug a chisel around, a bookkeeper will keep his finely crafted pen at all times, a farmer will carry a rake, and so on. Using the item to do damage will increase all assigned weapon skills, while performing the relevant task will increase the non-weapon skills.
Yes, I know it would create conflicts such as those that exist now between woodcutting and mining, but such problems should not exist, and should be fixed anyways, because dwarves can sure as hell carry several tools, even though they need a backpack for that.
As to "where to get those items for starting", I suggest that these items be put in for now, but their presence should not be required - although there probably should be no skill modifiers applied without the items. Once the game's internal mechanics are fleshed out enough to allow easy replacing of accidentally lost items, the requirement can be put in wholely. Them being "just put in" will be a first step, and a test phase to see how those items might be replaced.
Finally, what is the purpose of this as a whole? Amongst many other things (like having even your workers always be armed with SOMETHING), it will also be a step towards allowing an adventurer to use nonmilitary skills.