Hi there!
The best way to do this is going to be through a Material Parameter Collection. MPCs allow you to have one exposed global control that affects multiple materials, making it really good for things like player location, wind and weather effects, and also this.
Here’s a good video that breaks down what MPCs are and how to implement them (love this guy)
The only downside of this is that you’ll have to go through your master materials and manually add the lerping object to each one. Luckily, it should be pretty copy-paste.
I would also ask the question though- if you need to create a blend for the entire scene, have you considered using a postprocess material instead?