I believe that as long as you passed the minimum grade (which is what Jaune's transcripts were for) and make it through Initiation, you can become a Huntsman. Regardless of actual aptitude towards aura, if you can prove that you make the cut, then you make the cut.
"Hunter" is an entirely different job in Remnant, as we found out from the fact that Lie Ren's father was a regular hunter, as in someone who hunted animals for food. Huntsman is the proper term, and if you want to refer to both males and females, the show has had characters say "Huntsmen" as the gender neutral.
Anyway, while anyone who has their Aura unlocked can attempt to become a Huntsman, not everyone can, considering there's an entrance exam they have to pass to be enrolled in a Huntsman Academy. Ozpin said such in Welcome to Beacon: "As you know, in order to enroll at my academy, students must first pass a rigorous entrance exam. Most applicants spend years of preparation training at one of the many combat schools around the world."
I believe that, if someone has a low amount of Aura and can't increase it, they will probably try to tailor their weapon and fighting style to cover for that weakness. One way they could do that is by prioritizing evasiveness by using a weapon that is mostly designed for ranged attacks and training to be able to move quickly so they can stay away from their enemy and dodge attacks.
OK thanks for the clarification!