I wouldn't say "no guns = no vera".
Vera is a item.
Dependant upon the character, Vera could be a two-handed sword, a flail, or a repeating crossbow. It's really all dependant upon your concept. That and some hand waving.
I think Jayne's charisma was pretty high. His job was Public Relations, after all.
Remember, Charisma is more "force of personality" than "likability".
For wisdom....he had good senses and strong will. Not so much on the empathy, and he was pretty easy to trick...I'd call it 10-14, depending on interpretation and roleplaying.
After more thought, ranger with fighter multi may be good too. I think of when Jayne takes out and takes the place of the sniper. I'd make him a two-weapon ranger to get toughness and take powers that can be used melee or at range.
I think he'd most likely be a Ranger (either, but able to do both), or a Brutal Rogue.
Fighter may work, but the fact that it has no ranged abilities makes me not feel like it represents Jayne's versatility. Then again, this is pre-guns, so melee weapons are actually mildly useful...
I could see Jayne as a Ranged Ranger with a few up melee moves.
Vera could easily be a bow or crossbow in a fantasy setting, and for all his toughness, Jayne is excellent with shooting and sniping type attacks (as seen in the Pilot and 'Our Mrs. Reynolds').
I would go with the brutal scoundrel rogue, I think that fits him perfectly.
Just give him the toughness feat for his added heartiness, and focus on rogue powers that work with ranged weapons, and your good to go. You could also throw in the ranger multiclass to give him that "sniper" focus when he pulls out vera for the tough shots.