By "as little disturbance as possible" I assume you mean as quietly as possible.
The noise from any type of firearm or air rifle comes from the muzzle blast. That's the sudden release of gasses as the projectile exits the barrel. If the projectile size, weight, speed, and barrel length are all identical, then it doesn't matter what type gun it is, the muzzle blast will sound just as loud. The same amount of barrel pressure is needed to propel the projectile, and that same pressure will sound the same as it exits behind the projectile.
Your typical Canadian tire pellet gun is only imparting about 3 ft lbs of energy to the pellet, whereas a .22 rifle is closer to 120 ftpbs. So it's easy to see why one would think a pellet gun would be a quiet option, but when you start getting into any type of gun that will have the necessary power to kill a coyote, it's gonna be loud no matter what.
Maybe someday they'll let us use suppressors... Until then, it's either a bow, or a Leonidas worthy spear throw.