For most countries in the West, it’s already illegal for anyone other than the state to enforce judicial punishments, and when it comes to arbitration, civil courts already take precedence and can throw out any ruling by a Shariah court. Marriage ceremonies aren’t recognised by the government either unless a Muslim couple also goes to a registration office.
All that’s really left are civil courts and most places, so long as they don’t break the law of the host country, both parties can agree on any code or law, Muslim, Jewish, or even the Code of Hammurabi. I don’t see what you could ban other than private expression of Islam — the Shariah is all of the laws of Islam, like praying five times a day and abstaining from alcohol — or banning belief in these laws as divine in origin, in which case you’d be banning belief in Islam and creating thought crime.