I thought that as well!
...but you're probably going to be disappointed, because I looked it up, and apparently the Swedish word is just "Milkshake." It's not even spelled all cool like "Mjölkkäk" or anything like that.
Seriously, what's the point of having all these languages if they're all going to end up using the same words?
Oh well... JAG DRICKER DITT MJÖLKKÄK! sörpla JAG DRICKER DET HELA UPP!!!
Funny thing is "käk" actually is a Swedish ett-word. It's a colloquial word for food akin to "grub" in English. It's not pronounced quite the same way as shake though.
And just for reference, a correct Swedish translation for your phrase would be "JAG DRICKER DIN MILKSHAKE! JAG DRICKER ALLTIHOP!" The latter sentence more closely translates to "I drink everything/all of it", but there isn't really a straight, literal translation for that particular construction.