I dont have an expresso machine to try this, but why would you use hot expresso when you're shaking this with ice? Wouldn't all the water from the melted ice just turn the expresso in to room temperature coffee?
It is counterintuitive to use hot fresh espresso, but espresso that has been allowed to cool is more acidic and lacks the flavour of freshly made espresso. With good ice, over dilution is not an issue. However, if you don’t have an espresso machine, then there are some purpose-made coffee concentrates available, e.g. https://www.diffordsguide.com/beer-wine-spirits/6790/solo-coffee-cold-brew-concentrate