without the key you'll need to get the immobiliser inside the ecu reset so it can be paired with different keys (could probably use you existing keys one the ecu is reset). the ignition switch and antenna are not the issue.
the wiring harness may have different connectors in particular the one to the ecu. even if this plug is the same it may need repining due to different assignments. have a stare at the wiring diagrams on
https://manuals.wotmeworry.org.uk/Vespa/ and spend some time skimming through the service manuals
need to check things like where the coolant hoses will route. if your 125 uses an electric water pump you'll have to remove it as the 300s all have the water pump as part of the engine.
no idea about the rest.
not so sure it will be "easy" but of course anything can be done with enough effort