Note that the field of linguistics uses the phrase ‘perfect synonym’ to refer to what you mean by synonym, and when they say synonym they allow possible variances of nuance.
Anyway, it depends on how much variance of nuance you want to allow. (Does the fact that extortion is Latinate and blackmail is Germanic count for anything?) I’ve seen a claim that no language has truly perfect synonyms (i.e. two words such that P(X|someone says word1) = P(X|someone says word2) for all X in all circumstances), which might well be true, but which would make the phrase perfect synonym useless.
Anyway, it depends on how much variance of nuance you want to allow. (Does the fact that extortion is Latinate and blackmail is Germanic count for anything?) I’ve seen a claim that no language has truly perfect synonyms (i.e. two words such that P(X|someone says word1) = P(X|someone says word2) for all X in all circumstances), which might well be true, but which would make the phrase perfect synonym useless.