I would prefer to write this one as "I've switched off my laptop by pressing the shut down button". Yours doesn't seem right, and as I reflect on it further* I think it's because your sentence feels like the cause and effect are backwards. In my sentence, I've made it clear that pressing the shut down button is what switched off the laptop. Your example makes it sound like switching off the laptop caused the shut down button to be pressed.
*See what I did there? I said something doesn't sound right, but instead of just dismissing the sentence right there I explored WHY it doesn't sound right. As I'm sure you're all well aware, "sounds wrong" should never be used as a reason on its own for eliminating a SC answer, but for those of you who have a good spidey sense about the English language it can often help you identify where to focus your attention and your application of grammar rules. Think of it this way: if you hear a rustle in the bushes, that's no guarantee there's a bad guy lurking there, but if you're looking for a bad guy, that rustle in the bushes you just heard seems like as good a place as any to start your search.