You can modify the Trafficking activity tables to remove the "free" weapons that the activity gives you at the start. In SR3 the Trafficking tables are named _A_DT_*_*.xtbl.
The free weapons given to the player are listed between the <Weapons></Weapons> XML tags. Just remove <Weapon> entries between those tags that you don't want to be given. It's "technically" required for there to be at least one weapon in the list, but you can try removing all of the weapons and see what happens. It _should_ silently handle there being no weapons, but it might also cause the game to crash when you start the Trafficking activity.