彼女はショック死した。

English Translation

She died of shock.

is there a difference in connotation between 死する vs. 死ぬ?

@ericaw
I’m afraid you mistakenly split the phrase. ショック死 (noun) + する (verb) is the correct structure. It’s not ショック (noun) + 死する (verb).
If you want to use a verb 死ぬ, ショック死んだ is the correct structure. and you cannot omit the particle で from this sentence structure.

○○死 is a “cause of death”, and you can use the same ○○死 + する compound phrase in different causes such as:

溺死(できし)した = died in a drowning accident = 溺れ死んだ(おぼれてしんだ)

転落死(てんらくし)した = died by a fall = 転落し死んだ(てんらくしてしんだ)

病死(びょうし)した = died of a disease = 病気死んだ(びょうきでしんだ)

Please keep in mind, however, that ショックで死んだ and 溺れた死んだ etc. sound a bit impolite while ショック死した and 溺死した are totally okay.
I feel ○○死 + する is more descriptive from a neutral objective standing point (e.g. in a police case report or a newspaper article). But we usually avoid 死んだ as a verb and we prefer 亡くなった (なくなった) . It’s the same as the difference between “died of” and “passed away” in English.