For me, the problem with accident is that it seems far too easy to attribute it to just about anything. I mean, hell, if we look at Yugi, it could be possible to punch someone to death, like if in a fight and then you accidentally hit a weak spot or something. However, I reckon Remiel will be like TRPG and will try and make it obvious for us, so I think it makes sense to exclude things which are actual weapons, because if it were a weapon then he would have chosen a different type of death. So:
Yugi006: Punch, Sulfuric Acid, Arsenic, Gunpowder
Strangefate: Dagger, Pistol, Pesticides, Bite and Tear
Assassini: Trophy, Blender, Machine, Match (the fire kind)
Sherlock: Kick, Electric Current, Hammer, Work
Madame Professor: Packing Tape, Overdose, Mad Dog, Venomous Scorpion
BAMF: Injection, Towel (again?!), Illegal Drugs, Ice Skates
Verasaille: Pills, Poisonous needle, Dumbell, Plastic Bag
James Moriarty: Kerosene, Candlestick, Lighter, Electric Bike (like a vespa)
persephone325: Virus, Wrench, Drill, Video Game Console (The card shows a PS4!)
I've also excluded stuff like the poisonous needle and the venomous scorpion because I think "poisoning" fits those better. Whereas, it seems perfectly plausible that one could accidentally have too many pills.
That said, I reckon it's going to be hard to get past "Overdose" which is the only card which actively says "accidental death".