KaneTheMediocre

The nerf Kronos is just a great deal.  It's not exceptionally good, but it's both much cheaper and much smaller than all the other rival blasters.  Dart zone rival blasters are OK, but not really superior to the nerf rival blasters (unlike their dart blasters, which are markedly better than Nerf's).  The titanium and powerball use a little hopper, which works most of the time but fails to feed just often enough to be frustrating.  You can just use a rival magazine which should feed perfectly, but of course that's one more thing to buy and distribute.   Still probably works out cheaper than an artemis, which is the closest nerf equivalent (pump action), but the artemis holds more ammo and the magazines are a non-removable part of the blaster, which simplifies things.

If you're trying to supply for a big group I would also avoid battery powered blasters like the plague.  Blasters eat batteries pretty fast, and it will create a logistical nightmare even if you have enough spare charged batteries.  Not to mention the added cost.

And yes, the adventure force / dart zone rival balls are the best option.  They are something like twelve cents each, which is very close in price to the 3rd party online knockoffs, but the quality is just as good as genuine Nerf rival balls.  Exclusively at walmart unfortunately.

I would assume the dart head rubber would need to be iron impregnated in order to get enough iron to pick up the dart without making any part of the tip rigid.

It's not too tough a technical problem, but string tends to trip people so it's a bit of a safety hazard, and imagine trying to untangle a bin full of darts connected by string.  

Yeah, standard wheels should be doing 35k RPM; big wheels have been more like 25k RPM but either way thats way faster than a pull cord will get quickly.

I think you and I mean different things when we say "big".

So I don't do flywheels, but I know a few things about electronics and feel I need to explain some things.

The capacitor you need to do this probably costs more than the bigger battery, without giving you any increase in capacity that you would get with a battery.  This is kind of a weird edge case where it's probably not absurdly expensive, but still more expensive than just using a bigger battery. 

Neither solution means you'll have a fast spinup time, it just means it will be as fast as it can be for those motors and wheels.

The pullcord solution might be viable with larger-than-normal flywheels or a geared system, but making it work will again cost more money than a big battery.