Let $\mathcal{H}$ be a certain kind of Hilbert scheme of curves on some smooth projective variety $X$ and $\mathcal{H}$ is projective and irreducible of dimension $3$. There is a divisor $\mathcal{D}\subset\mathcal{H}$ and $\mathcal{D}$ is a ruled surface over a curve $C$ (not necessarily smooth). Let $P\in C$ be a singular point and let $F$ be the correspondent fiber and $\mathcal{H}$ is only singular at $F$. Let $\pi:\mathcal{H}\rightarrow\mathcal{H}'$ such that $\pi$ contract $\mathcal{D}$ to $C\subset\mathcal{H}'$ and $\pi$ is isomorphism outside $\mathcal{D}$.
What information or property I should know to show that $\mathcal{H}'$ is also a projective. In the smooth setting, I can try to show that $\pi$ contracts negative $K_{\mathcal{H}}$ extremal ray and apply Cone theorem to show $\mathcal{H}'$ is projective. But now $\mathcal{H}$ has singularity and I do not know whether the singualr locus being a curve (actually $\mathbb{P}^1$ in my case) would belong to some class of singularities(say klt, lc,etc) to allow me apply Cone theorem in general.
