I'm sorry, but isn't really knowable. Assembling a sampling of people wealthy enough to own slaves would be a tremendous project because you'd have to go straight into the census microdata to get the value of their assets. Then you would need a firm idea of how much a slave costs...but there is no set, going rate. It depends on the age, sex, health, and skills of the slave as well as time and place. That's a fiendishly complex thing to nail down, though there is recent effort at doing so.

I can't give you a number, even to ballpark it. There are certainly many southern families that want slaves and can't afford them; slaves are an aspirational purchase as well as a strictly economic one. Owning a person is a way to show that you've made it and are, however marginally, a person of substance. That's probably true for most of the white South, most of the time.

There are always individual exceptions, though they are pretty rare. -If they weren't, southern politics would look radically different.- The best place to look for them would be in isolated hinterlands far from the major plantation regions, basically the upcountry, interior South. These are places where, at least until Reconstruction, the infrastructure to transport out crops of the major southern staples (cotton, but also tobacco and hemp) just doesn't exist yet. West Virginia, eastern Tennessee, and western North Carolina come immediately to mind here, but with the exception of South Carolina every state that seceded in 1860 has at least some small white belt regions to contrast with the black belts.

The choice not to own people, for those who are financially able, would come from several different places. There are always a few who believe slavery personally distasteful or unwelcome. Probably a whole lot more hate the idea of living near to black people, both for the usual white supremacy reasons and a related set of ideas about how the enslavers and enslaved are natural allies who somehow use their power in state governments to underdevelop and isolate the upcountry, while taxing it unfairly. Not owning people, or owning fairly few (say, less than you could afford or use) could be a political statement in that context.

But it doesn't do to take this too far. Andrew Johnson owned a small number of slaves despite a political career where he sold himself as Mr. Eastern Tennessee. When West Virginia tried for statehood, its initial constitution maintained slavery. DC told them to go back and abolish or they could forget it, which WV then did. Even in the white majority, non-plantation South small numbers of slaves are fairly common and there's a strong reluctance to challenge the system except as a tactic to get some kind of unrelated concession out of the state legislature. People would not, most of the time and in most places, go around saying that their decision was a political or moral one. (Maybe in the most marginal slave states, like Maryland or especially Delaware, but it's a really heavy lift.) That kind of talk could get you run out of town, occasionally even assaulted. All of which makes it very hard to isolate people who would have made such a choice in the historical record.