According to several experts, Quercus nigra is not one of the many oak species considered to have allelopathic properties. However, they do have an extensive fibrous root system very close to the surface of the soil, making it difficult to grow plants and grass nearby.

If the trees offer value to the property, and I would think that they would in SC, you may want to consider using mulch under these trees, rather than disturbing the soil/root system.

By the way, Water Oak is a common name VERY often used for another oak, Quercus laurifolia (Laurel Oak). In parts of SC (where I lived for over 20 years), Q.laurifolia was nearly always called water oak. But, whichever one you have, you'll be safe from allelopathic problems.