I think it would be
cholesky!(Symmetric(copyto!(C.factors, K), :U))
The matrix that actually stores the data for the Cholesky object is the factors field, either in the upper triangle or lower triangle according to the uplo field. If you copy the contents of K to C.factors and then force it to be considered as Symmetric stored in the upper triangle (or lower, if that works better for you) then the cholesky! method will decompose it in place.