Recoilless Railguns

[Steel]

If you want your railgun to fire a 10g projectile at 1km/s, and it has a 1m barrel, that requires a constant acceleration of 500,000m/s^2, and therefore a force on the projectile of 500N, or the equivalent of a 50kg weight sitting on your shoulder for the 0.002seconds it is in the barrel.

No way of getting around this, the lack of propellant makes no difference. The bow and arrow has less recoil because it fires a heavier projectile much much slower and over a much longer time and the force on the arrow decreases as it accelerates and the string is less stretched, all making it feel lighter once the force you were holding against starts to decrease.

[HMS Conqueror]

By conservation of momentum, something must recoil with equal and opposite momentum to the projectile. The question of what is an interesting one and not entirely simple to answer, but whether something does or not isn't a discussion. There's no way around this, even with rockets. In the case of the rocket, the exhaust recoils.

btw, I'm not entirely sure if it's serious, but railguns are going to be large gun emplacements, not small arms, until long into the future. It's a question of energy storage.