What if the reason that Hux walks like he has a stick up his ass is because he lost is 2 legs =))))?
Remember the inductions test of the Commandant’s Cadets where prospective cadets were recquired to kill another cadets and make it pass as an accident? What if Brendol Hux decided to put the life of his son on the line resulting with Hux ending up badly injured because he was not cautious enough with his fellow comrades?
The prosthetics and the pain that comes with it is a reminder of his own weaknesses for him and the event made Hux even more paranoïac and ruthless.
This is why he also tries to avoid battlefields.
Since he tends to keep up with apparences, only few people knows about his lost limbs and he know how take care of his repli-limbs since he is an engineer