To this, it's important to get the questions answered in order.
When did Zenos obtain Resonance?
-Well... if we're to assume he used the same source Fordola's came from (Krile), it would have to be between our duel in Yanxia and when we returned to Eorzea.
Is Resonance what let Zenos wield his enchanted katana?
-Probably not. Even during the duel with him in Rhalgr's Reach, he was already using the Storm and Swell to produce lightning bolts and bursts of wind. I don't remember where, but one of his bios mentioned he was already augmented before the events of Stormblood; assuming aetherial conductivity is necessary to wield enchanted katana like Zenos does, Aulus probably made that possible for him.
Side note: though he uses the same weapon(s), Zenos fights nothing like a SAM unless you consider some of his techniques to be hyper-augmented versions of SAM abilities (Storm, Swell, Sword being a massively enhanced Midare Setsugekka, f'ex).