I only use the word nor when I pair it with the word neither. This is not a strict grammar rule, but it is correct, common usage.
Your sentence should be: "...not for John or me." If you said "...not for John nor me." I would consider it non-idiomatic usage. If you said "...at least for neither John nor me." I would consider it non-idiomatic and awkward.
When I refer to "idiomatic English," I'm referring to the natural speech of native speakers. That speech may or may not be grammatically correct. Many native English speakers where I live will utter a sentence like, "Them peoples is stupid." This sentence has several grammatical errors, but it is idiomatic (non-standard dialect) English and every other native English speaker will understand its meaning.
If a person says, "The laces of the shoes that are mine can be joined together through the utilization of abilities that are my own," his sentence is grammatically correct, but non-idiomatic because no native speaker would say that instead of some form of, "I can tie my own shoes."