If you look at the actions of politicians like Merkel, Sarkozy and Rajoy, it is pretty easy to see that it is unlikely that one day they will suddenly grow a backbone and say “let’s all do a firedrill currency change over the weekend!”
The lowest friction way to a new currency would be to just start issuing IOUs for Euro, and use these to pay for services (California did this a couple years ago and it turned out not to be a big deal). In fact, they could even make these IOUs in handy denominations and on fancy paper so that people can use them to pay for stuff. The government could pass a legal tender law to make it so people have to accept it where they would normally accept Euros.
Effectively it creates a second currency that circulates along with the normal Euro. This already happens in the UK with the Scottish bank notes, and no one complains about it much. (Strangely enough, the Scottish bank notes aren’t even legal tender)
This might even stimulate the economy, as everyone tries to spend their “fake” Euros as quickly as possible. In fact, Gresham’s law would suggest that the new pretend Euro would become the primary circulating currency as people would tend to hoard their Euros or send them out of the country.