The original cause of the fuse blowing was that when the tank set was being removed from the Apollo 10 SM due to some electromagnetic interference concerns. During the removal, a technician failed to properly remove a restraining bolt, and the shelf fell 2 inches. This jolt is what damaged the fill/drain port that then lead them to try and use the internal heaters to boil off oxygen during ground testing. That, in turn, lead the fuse to short and the wiring to burn off its insulation to create the conditions for the accident. Butterflying this is easy--have the tech notice the bolts and properly remove it, and the tank set is never dropped. No drop, the fill/drain port isn't damaged, and they never have to try to boil off the oxygen with the internal heaters. Don't do that, and the insulation doesn't burn off the wires creating the explosion risk. There's a pretty solid chain of causality that can butterfly this if you want to.
Apollo XIII's accident is a lot simplier than what happened with Apollo I. The fire'll still happen; when you put 100% oxygen in at too high pressure something's going to burst into flames sooner or later. As high as NASA had it, oxygen toxicity would kick in if the crew wasn't properly sealed in their suits. I remember reading that it was pressurized to over 1 bar, but find that hard to believe. 1 bar of oxygen will make anything burn.