Solution:

The primes between $4$ and $18$ are $5, 7, 11, 13,$ and $17.$ The product of two of them is odd and the sum is even, so $xy - (x + y)$ is odd.

Since $xy - (x + y) = (x - 1)(y - 1) - 1$ increases as either prime increases, the result ranges from $5 \cdot 7 - 12 = 23$ up to $13 \cdot 17 - 30 = 191.$

The only odd option in $[23, 191]$ is $119 = 11 \cdot 13 - (11 + 13).$

Thus, the correct answer is C.