I really liked that idea!
Like ALOT! a father-point to you my good sir!
One thing to consider regarding your firing-control is that it would probably take a while from pulling the trigger to get any effect down that pipe, and the first few seconds of effect will not be at full power, since your system will have a "large" volume of air in front of the fans to compress and accelerate before it exits the muzzle, before bringing the air speed up to max.
I think i personally would have used a electric ducted fan from a R/C plane instead tho, as i belive it would provide better pressure and smaller form factor, prehaps even fit it inside a semi-bulky weapon.
And regarding that battery requirements; im dont know the age and temper of your son, but mine would probably not release that trigger if his life depended on it, and later be quite upset when the batteries run dry.