I think you need to ask yourself if you want to allow people to play your game on computers that are not online 24/7? Otherwise you add the condition that the computer has to have an internet connection just to play your game. And it's not always going to be the case.

So if you do want to allow people to play while not online, you have to choose the alternative means. A) Have an Offline Highscores list OR B) Just don't save the highscores anywhere.

Best to keep your solution simple and to the point or you'll just run yourself in circles and make a mess of it's implimentation.