I hope my comment is not unnecessary or irrelevant, but I need to point out the following.
Crossbows:
Mechanical energy storage is feasible in the DF setting. Case crossbows. A crossbow can remain loaded for quite some time and discharged later. And for those that want a repeating crossbow, I recommend a hand-cranked thing that repeatedly pulls the sting back and lets it fly while you turn the large wheel on the side. The torque should make this easily possible. That said, a crossbow modified to shoot a spinning disc is really no stretch of the imagination. However there is also no major need for spinning discs, as we have crossbow bolts.
I think you're missing the point of a crossbow bolt. Put a rock in a crossbow instead of a bolt, you have a weapon that delivers a nasty bruise, nothing more (maybe a broken bone at close range). If you put a lot of energy into making a blade spin, 3 things will happen:
1. The blade will lose energy fairly rapidly to wind resistance. Compared to the fairly streamlined design of an arrow or bolt, discs have a lot of surface area.
2. You won't be able to spin the blade fast enough to cut. You might end up with some minor slashing wounds, but unless you nick a surface artery (such as the neck or wrists) odds are the wound won't even be felt through the adrenalin rush. If you had a bladed disk instead of a serrated one you might have better luck, but it still would be easily stopped by even wooden or leather armor.
3. The blades will be less accurate. While the gyroscopic forces on a frisbee would make it fairly accurate, they're nothing compared to the accuracy of a straight projectile.
Ranged weapons don't really carry enough energy to slash, you have to focus the energy into a very small area to cause damage. There's no way in the 1400's for technology to create a handheld device that could launch a spinning disk fast enough to be lethal. Possibly a siege weapon could do it (though why you'd bother I don't know, a ballista would still be far more lethal), but not a hand held crossbow.
I personally feel that springs are badly out of place in the DF world. They aren't period appropriate, and they don't seem very dwarvish. Dwarvish breaks from reality tend to be into a fantasy realm, not into a level of technology several hundred years more advanced than the game's setting.