Unfortunately, there's only the single set of tools. So, if you lack the feat to equip them then you can't gain the benefit of their use, obviously. This doesn't stop you from performing any of the crafts we have with the exception of Smithing, however. Lacking the feat(s) just means gathering the supplies for the craft may take considerably longer.
Also, for mining in particular, the more attacks you can perform in a round that overcome the rocks DR, the faster you get ore. So, I highly suggest people wait until they at least get there second or third attack before attempting the craft as anything more than a passing interest. Either that or grab a mage that can spam haste to expedite the trip, but even under both of those circumstances, mining is still a very long process. I usually go semi-afk and make a sandwich or do a little cleaning while I wait, peeking over every now and again to make sure nothing's trying to eat my mook.