I think specifying explicitly, “absurd fantasy violence” or the like, is the best option. Someone who has a trigger about, say, violence against animals, might still want to avoid it even if it’s done in Looney Tunes style, but someone who doesn’t want their impressionable young children imitating things doesn’t really have to worry about dropping anvils on people’s heads.
“Genre-typical” is a very useful term, imo, because Looney Tunes murder and Agatha Christie murder and Shakespearean tragedy murder are three very different things, and I’d struggle to explain that difference in a nice concise CW without being able to resort to “genre-typical”.