Om det er noblere i sindet at tåle
Forargelig skæbnens stene og pilene
Eller at trække sværdet mod et hav af sorger
Og ved at modsætte sig standse dem
Wow, I didn't consider that before, I wish I could give you a lingot, but I am on mobile so take my appreciation!
Not exactly, Danish pronunciation has changed since then as much as English pronunciation has. (And the original story goes back at least to the 12th century and would have taken place several centuries earlier.) But certainly closer than what Shakespeare wrote!
I also (apart from Hamlet I mean) have a question, is it possible to say "At være eller ikke være?" (i.e. to skip the second "at"). That's how we say in Swedish "Att vara eller inte vara".