If so, are they antonyms or did one undergo a lexical shift to become the other? Also, is the /es-/ prefix used as a negator in any other English words, or is this case an exception?
No, the two words are not related. There is neither a direct relation nor a negation.
"Shew" is an old version of "show" which comes from proto-Germanic "skauwojan", i.e. choose, look at, and other verbs. Even in Proto-Indo-European, there is "skeue", pay attention.
On the other hand, "eschew" is from proto-Germanic "skeukhwaz", i.e. escape.