I completely understand not being able to draw. But when building things that have never existed, it can actually be worth the effort of first learning how to draw. Specifically, learning proper drafting techniques to produce technical type drawing. I've always been a miserable drawer, and I still am, but I've been teaching myself to draw by skimming through public domain Google Books on drafting and technical drawing, and reading/copying images from US Patent Applications.
Alternatively, you can teach yourself to use CAD software, but the friendlier software tends to be pretty expensive (thousands of dollars, yikes!), and a lot of the resources for learning it are expensive too.
So if you want something to be realistically practical, as opposed to a genius with infinite resources Iron Man type design, then you might be overdoing it a little. In this scenario, you want something that could be made with few resources, using mostly scrounged parts. You want to stick to mostly proven designs, since they will be more reliable, and you want the finished product to be lightweight, so it can be easily carried on foot, and can be quickly drawn, aimed, and fired.
An arrowhead propelled by a spring on rails wouldn't work well, as it would tend to not fly straight without an really long rail. This is part of why musket barrels were so long. It would force the ball to build up a straight path, and it would let the gases apply as much velocity to the ball as possible. A spring propelled projectile with have a much slower velocity than a musket ball. Plus, if a ball tumbles about, it doesn't matter, if an arrowhead tumbles, it will go off course with wind resistance, and it will not strike with the pointy bit.
The disk shooters only work as well as they do because they first put spin on the disk, like a frisbee. This mechanism would only be deadly if you gave it a razor sharp edge, and that would be a very customized and labor-intensive projectile.
I'm not sure what you mean by spindle. I know of 2 major types of pitching machines. One uses rubber fly-wheels spaced one ball-width apart spinning in opposite directions at high velocity. The other uses a long lever-arm, spun at high torque. The first one would either require lots of power to keep the wheels spinning, or lots of time to spin the wheels up to full speed for every shot. The second would have balancing issues. Every time you tried to launch a projectile, the weapon would leap out of your arms, and likely smack you in the face.
It sounds like what you would really want would be some form of crossbow along with the tools needed to fashion your own bolts.