How could I do this in XAML?
XAML is a markup language and you cannot really call methods in it. You could bind to a method using an ObjectDataProvider as described here: http://www.devcurry.com/2011/03/wpf-4-using-objectdataprovider-for.html
But if you want to do something when a button is clicked you should bind to a command of a view model and call your static method in the Execute method of this command.
Trying to everything or as much as possible in XAML just because you can and just for the sake of eliminating code is generally considered as an anti-pattern.
MVVM is not about eliminating code, it's mainly about separation of concerns and C# is a much more expressive and more concise language than XAML. So you should implement the behaviour of your application using a programming such as C# language and use XAML to define the visual presentation and the layout of your UI.