I'm using the Redding S-Type Full sizing bushing die with my .308 rounds. It's came with an expander ball and a non-expanding deprimer pin holder. I use it for neck sizing without the expander ball, since I've neck turned my brass and don't want the ball mucking up the neck concentricity. Although Redding makes a very uniform die, I don't want to take the chance. It seems to work well enough.
Can't say if this will affect the Hornet brass. You may want to contact Redding directly and ask, or the fine folks here may have a better answer for you.
Regards,
S.