Lol, yes, I get the impression v_v_lala is not looking for "Katte gets life imprisonment, is disillusioned by Fritz's paranoia in 1740, ends up in England." :P

Well, quite. Unfortunately, the way my mind is wired produces only the following „Five Ways Katte lives“

1.) Fritz dies, Katte lives, Wilhelmine avenges. (I.e. Fiat Justitia)
2.) FW accepts the war tribunal‘s sentence for Katte, Katte gets freed and honored in 1740, but he and Fritz are so different people now that Katte ends up disillusioned and ready to start a truly new life in England.
3.) Katte never leaves England the first time he‘s there, despite Dad‘s objections, befriends Fritz of Wales instead of Fritz of Prussia, gets involved in Hannover drama accordingly, which doesn‘t end lethally but with bitchy memoirs. Meanwhile, Hervey‘s way back from the Grand Tour includes a stopover in Prussia where he befriends Fritz of Prussia. This leads to Fritz developing a very different literary taste which includes Shakespeare! But he never meets Katte. Hervey certainly has no intention to die for so sweet a prince, though. His solution is to tell all to the Queen.
4.) Katte does everything as in canon until the point where he gets his warning. Then he hightales it out of Berlin poste haste, leaving all the papers unburned. This means FW gets to read a great many letters between Wilhelmine and Fritz with uncomplimentary passages about himself, is accordingly even more angry when Wilhelmine volunteers as tribute Tries to plead with him and doesn‘t just hit her once, he hits her repeatedly, which leads to Wilhelmine dying of the results. Fritz never forgives himself or Katte for this and does not want to see Katte ever again.
5.) Katte reports Fritz‘ escape ideas to FW the first time he hears them. FW reacts mildly, for FW, since there is no grand conspiracy and his soldiers are pleasingly loyal to him, not Fritz. Which is to say: he taunts Fritz some more, but no one gets locked up, let alone sentenced to death.
A year later, Fritz doesn‘t commit suicide, no, but when forced to participate in another hunt, he has an accident with a gun that results in his death. There are a few sad poems, and otherwise his life leaves no traces in European history.

5a) Not applicable even if v_v_lala were a break it differently type, since she has time travel in her DNWs: Fritz discovers time travel the way Fredersdorf does in my other story, travels back into his younger self‘s body and DOESN‘T befriend Katte. Instead, he treats Katte to the full Old Fritz verbal onslaught the first time Katte makes an overture, knowing that if Katte never befriends him, Katte will live. Katte does live, marries (as the oldest son), and has an unremarkable but mostly happy life far, far away from any Hohenzollern. Fritz loses his memories of the original timeline the moment he‘s changed it for good and so never knows what he‘s missing or what he‘s gained, either. He still tries to escape, of course, and still fails at it, but because he tries to escape with Peter Keith a few months earlier, it‘s Peter who gets executed in front of him instead. Otherwise Fritz‘ life is exactly as in canon.

Conclusion: Fritz/Katte is not a pairing a Fritz/Katte shipper wants me to write!