I hate the whole "Condition" thing.
It's a single action semi-auto. It's made to be carried with the hammer cocked and the thumb safety engaged. There is no reason to carry it any other way.
There is absolutely ZERO reason to carry a 1911 or HiPower with a loaded chamber and the hammer down...no reason ever. Chamber a round and put the thumb safety on. Take the thumb safety off just before you're ready to pull the trigger and ride the safety with your thumb while shooting. Practice it enough times and it becomes completely automatic and involves no brain power or thought. Your body just does it automatically. I've never "forgotten" or had trouble taking a thumb safety off a 1911, HiPower or Remington 870 including in times of extreme stress. This worry about thumb safeties on the aforementioned guns causing problems or somehow keeping the gun from being fired intentionally are nothing more than internet speculation and foolishness. In the dozens of officer involved shootings involving the 1911 I've heard about, studied or personally witnessed not once has anyone ever had any issue whatsoever with a thumb safety.
...and yes, I've had the idiotic concerned citizen in a store or restaurant tell me more than once, "Officer, did you know your gun is cocked?" My only reply has always been, "Yes I do. It's supposed to be."
The firing pin safety was introduced to the HiPower mid run of the MkII guns and carried over to the MkIII. Like the 1911, I don't thing they're necessary, but I also don't think they hurt. The hammer accidentally falling is typically not the issue on the 1911 or HiPower when they're dropped. The issue is sometimes a worn out, modified or too light firing pin spring allowing the firing pin to fall forward under inertia if the gun is dropped on its muzzle causing it to strike a primer and fire the gun. Keep a strong firing pin spring in the gun (change it with the recoil spring) and it's typically a non-issue.
Since I don't have a Springfield Armory produced P35 nor have I had the chance to inspect one I cannot tell you if they have one or not. I would guess that they do.