We had a belt replaced in Martinique during some Hurth gearbox work. Yes, you need to separate the Vetus shaft coupling. You do not need to lift the engine. The AMEL mechanic just moved the engine back a little by slackening the engine bolts. It didn't alter the engine alignment.
If your replacement belt is good then you could easily leave putting a spare on until you need to change the Vetus coupling joints. They should last a few years.
Ocean Hobo SN96