Once again, I appreciate all the feedback.
I, too, will veto a character if I dont like the concept enough but its rare, admittedly. We have banned Orgasm as well, as it was once used in a way that creeped out the whole table. Got rid of Leroy Jenkins and Hobo with a Shotgun too. I'm ok with characters wylin' out once in a while, but not when the mission is an honest attempt at serious.
I have spoken with the player of the self-proclaimed "Thundercat" and indicated that no self-respecting Johnson would hire someone so ... 'colorful' ... to do anything clandestine. This lead to a conversation of what we each find fun. Player said he likes his characters to have something unusual about them so he has something to roleplay. He feels he's been in SR too long and has done everything there is to do.
I understand the sentiment to some degree. Not much I can do for the one guy if the whole group is still digging the game. I guess sometimes you have to pick your battles.
Well, now you know why he was running "thundercat"

I you are on board, here are some ideas you can throw his way if he is looking to spice things up.
1: A character with a "Moral" conviction. These can get interesting to play, as SR is a very morally grey game, where players have to sometimes do morally bankrupt things in order to achieve a good... but what happens where a character refuses to compromise their moral convictions??? Refusing to kill, and refusing to lie are two good ones, as technically you don't need to do either to achieve most goals in SR (its just that killing and lying are easier!)
2: "The long term planner:
when asked "why are running the shadows" most player runners give a flowery response that really boils down to "Get money, kill shit, bang bitches. Repeat". Or, it's some hyperly vague "me need revenge, because reasons!" approach. ** and really guys, I'm to blame here too, I don't give more then a paragraph motive for anything a character does anymore**
Having a clear cut, yet complex goal that the character seriously works towards, instead of a nebulous reason, can help focus a character and a player. "Me need revenge cause bad man stubbed my little toe" gets old by the 2nd time... "My character is raising money to build a orphanage that will be run by the local church because he was an orphan as well" can give a player a lot more focus as he now has various tasks and milestones to reach.... other than shooting something.
3: "Little man up" style game play can be interesting for an experienced player. SR creation assumes the players have already cut their teeth in the shadows, and are professionals. But what happens when a professional gets pulled in to the shadows?
This style of play works best for someone with a ancillary profession to the shadows. Fire-fighters, paramedics, tourism outfitters, investigators, construction workers, and so on. You build the character based off of the profession,. with no illegal and limited restricted gear (a tourism outfitter might have a hunting/pistol permit, etc), that somehow end up in the shadows. How do their occupational skills come into play on a run? Some do surprisingly well! others not so much.
4: "The Elitist" style works best for combat style characters. They focus down one, and only one method of combat, and then work out ways to bend the combat to suit them. This could be like your sword guy above, but he should have the additional tools and skills to back up that style of play. For example: (sticking to the swordsman build) Character makes use of smoke grenades to provide cover to close to melee range with ranged combatants. A pistoleer may use subtly and palming to sneak a weapon close to a mark, and/or parkour style skills to get away/ close in to firing range.
Whatever their chosen "elite" Method, they have the complimentary skills to make it work every time. Which takes a LOT more planning and fore thought then simply writing "armed combat 6 (combat axe) 8 on a character sheet! The Player should be asking themselves "If the target is at 'X' distance, what do I do?" for every single range interval, and have an answer. (even if that answer is "throw smoke grenade and advance"). He should also be asking " If I am attacked at "x" range, what do I do?" and again have an answer.