You would have to create a new contract, and broadcast to people that they should use the other contract. All these systems heavily rely on decentralised reputation - not just for users but for contracts as well.
It's not actual blockchains they're finding useful. It's the reasonably robust framework that people are building around it, where they get a whole lot for free and just need to optimise that annoying blockchain bit in the middle. Rather than do all of the crypto, security R&D they would need to do by not using 'blockchain technology' they just turn off the mining and get it all for free.