The "New Super Mario Bros
DS" mini-games, with the stylus (like carrying the bombs around, and whacking the moles) scratched my first screen protector.
Thankfully I had a screen protector. (It was a cheapy one, hence the scratching.)
I then invested (what like 5 bucks at most?) in some GOOD screen protectors as I didn't want to scratch a screen protector every other day and have to change it. I have had the same screen protector on for MONTHS. Literally, since before May. So that's at least 6 months. (I got those screen protectors at Wal-Mart.)
I don't know if Zelda will scratch your screen, but my recommendation is get a screen protector and then you don't have to worry about it at all!
(And if you haven't used screen protectors before: they are easily applied and easily removed, so no worries about them sticking to your screen and leaving an ugly/sticky residue.)