Do Historically Black colleges and universities have Affirmative Action programs to take more non-Blacks?

No, HBCUs receive funding if they have a certain percent of minority students. Given that the schools are historically black, most of the students are minorities as well. HBCUs, in the exception of Howard, Morehouse, Spelman, and maybe Hampton, are generally easy to get into as long as you apply early and graduate from high school with at least a 2.0. Schools may recruit white players in sports such as golf, swimming, tennis, and volleyball from abroad because not many African American students play those sports. African Americans who do play those sports often go to bigger schools, like Ohio State, Florida State, Texas, ... I think you would have a good chance of getting accepted into the school. Affirmative Action does not play a role at HBCUs.