Someone using an illegal weapon in a match presumably viewed by so many people should likely have some manner of consequence. Stations and the like may look the other way so long as the player is using the weapons against potential threats, but using a waste cannon so blatantly in a match ought to result in some sort of response.
It should be like pro wrestling- pro wrestlers who use illegal moves in the ring tend to keep wrestling but are seen as "bad guys". Obviously Katami wouldn't approve.
Since you've already demonstrated that you're ready to play dirty, maybe the Black Market could approach you directly with a payoff to throw the Slicer match instead of kidnapping Katami to get your attention. Payoff could be cash or a nice little gift basket of illegal drugs and military equipment.
If you take the bribe, the Black Market creates an illegal clone of you which dies in the ring and you get issued a new fake identity, resetting all your faction levels. And Kate could be VERY surprised if she runs into you later on...
I like that idea a lot. I was thinking that there could be 3 possible solutions, ranging from easiest to implement to hardest.
The simplest is simply to ban a player that uses illegal weapons from the Arena, confiscate the weapon, and fine them.
The moderately simple solution is to modify the player's standing with the crowd, marking them as a 'heel'. Heels would be given harder opponents and be hated by the crowd, but would be offered more money to fight. Katami would likely abandon the player at that point, making the Katami mission not appear. Instead, some Molotoks(or their lighter variant from CC) could ambush the player in the middle of their second to last mission instead.
The most complex solution is something like what you indicated, serving as an alternate route into the Black Market that serves as an alternative to the Katami mission.
Note that this would make more sense if it were likely for the player to have illegal weapons already installed at the time they reach the arena, since right now only a black market shipyard will install the waste cannon or neuroplague launcher and it's a pretty long way from Rigel to the nearest BMS.
Consequently, for most players not already aware of the possibility of being a heel, this could only be triggered by using Reapers- and the Revelations-class is vanishingly rare before Rigel.
Also, there should probably be some sort of reaction to a player in Iocrym armor lamplightering all opponents. Either a regulation on equipment level that prevents this or a special trigger that just gives you the championship fight after one battle with a very OP loadout.
Fixed in 1.9 beta 4.