Since moving photons have momentum, am I right to suppose that light from stars is able to interact with (and disperse, if intense enough) clusters of dark matter?
Dark matter is totally transparent. A photon passing through dark matter will not deflect dark matter through collisions.
Dark matter only interacts with gravity. As my2cts pointed out, that means dark matter and light can interact. This usually would mean that light can be deflected when passing by a massive enough object, such as a galaxy or cluster of galaxies. This deflection is caused by the curvature of spacetime. Light is deflected in the sense that it follows a curved geodesic, not that it is deflected from a straight path by a force.
But for light to deflect dark matter through gravity, light would have to be a source of gravity. The sources of gravity are energy density, stress, and pressure. Starlight is far too dim for this to any measurable degree. It might have an impact in the interior of the brightest stars.