Because I felt like it, I want to give a rundown of the traits and which ones will actually do anything in this module:
Basic
Ironman: Yes
Finesse: Yes
Hellrunner: Yes
Tough as Nails: Yes
Son of a Bitch: Yes
Son of a Gun: Yes
Reloader: Yes
Eagle Eye: Yes
Brute: Yes
Advanced
Juggler: Useless, since both weapons are cursed and the stick has the same damage as a normal fist attack.
Berserker: Yes, but you need Brute 3 for it to have any effect, since melee hits must break the 10 damage barrier to proc berserk.
Dualgunner: Useless unless you are going for Bullet Dance or Gun Kata.
Dodgemaster: Yes
Intuition: Yes
Whizkid: Yes, but Armor/boots only.
Badass: Yes
Shottyman: Useless, obviously.
Triggerhappy: Useless unless you are going for Bullet Dance or Cateye.
Masters
Blademaster: Yes
Vampyre: Yes
Malicious Blades: Useless, the sharp stick is not a blade.
Bullet Dance: Yes, but requires otherwise useless traits.
Gun Kata: Yes, but only the fire time reduction, and it requires otherwise useless traits.
Sharpshooter: Yes
Army of the Dead: Useless, obviously.
Shottyhead: Useless, obviously.
Fireangel: Useless, due to a bug in the core game at this time.
Ammochain: Useless, obviously.
Cateye: Yes, but requires otherwise useless traits.
Entrenchment: Useless, obviously.
Survivalist: Yes
Running Man: Yes
Scavenger: Yes