The recorded English-language etymology for "ketchup" suggests that the word comes from one of the Chinese dialect's word for tomato. Do you have any idea which Chinese word sounds like ketchup?
茄ke2 汁zap1, but if I remember it correctly, Dan Jurafsky believes it is from 喼git1 汁zap1, worcestershire sauce
Not exactly a Chinese dialect, but Vietnamese calls tomatoes "cà chua": https://en.wiktionary.org/wiki/c%C3%A0_chua .
possibly Hokkien 膎汁 (kê-chiap, “fish sauce”) via Malay kecap ~ kicap “any dark clear sauce from soy, fish etc”
My personal theory based on nothing more than the vibe of the thing is that it comes from the Malay/Indonesian word ‘kecap’ (which is pronounced almost identically to “ketchup”), the word for sweet soy sauce. This is soy sauce that is thickened and sweetened with palm sugar, and I could see European cooks attempting to replicate it based on the vague descriptions given by sailors, and ending up with ketchup.