The answer is C. -0.9276.
We know that $\sin^2(\theta) + \cos^2(\theta) = 1$ for all angles $\theta$. Substituting $\theta = 4$, we get
$$\sin^2(4) + \cos^2(4) = 1.$$
Since $\cos(4) = -0.3$, we have
$$\sin^2(4) + (-0.3)^2 = 1.$$
Simplifying the right side, we get $\sin^2(4) = 0.91$. Taking the square root of both sides, we get
$$\sin(4) = \pm \sqrt{0.91}.$$
Since angle 4 is in quadrant II, the sine of the angle is negative, so $\sin(4) = -\sqrt{0.91}$. Rounding to ten-thousandths, we get $\sin(4) = \boxed{-0.9276}$.