A complete rebuild when an upgrade will do. Many agencies propose redoing everything as soon as they see old software. That takes months and costs several times as much. In most cases the existing code can be adapted, and that is what we suggest first.
Simply switching the version at the host and hoping. That is exactly how booking systems and shops go offline on a Monday morning. Without testing on a copy, a PHP upgrade is a gamble with your revenue.
And an open hourly rate. After the code check you get a fixed price. If the work turns out to take longer, that is our risk, not yours.