Not easy to find and more sensitive to moisture damage. I believe S&B is selling them for reloading. Note that the DDNT used in the NT (non-toxic) primers I am familiar with has higher brissance than lead styphnate primers, so flash holes may need to be drilled out to about 1/8 inch when using them. Check with the maker on that point as the formulations may have changed.
I don't think there is an advantage to an HP. It will still splatter lead on a backstop, too. An open base may experience a little gas cutting splatter, but the lead from the primers is a stomach acid-soluble compound and is much more toxic than metallic lead and so good ventilation and the primers should be the first focus. For NT bullets, a totally enclosed bullet like a plated bullet is better. Call the bullet makers to ask what they recommend in their lines, specifically.