I'm afraid the stylus would wear on the screen. My sister has one and the damage shows. You would be correct if it was a GBA SP, though.Do you really need one for a console with a clamshell design? close the lid and the screen is protected when the DS is not in use. If anything a case would be better to keep the DS in when not in use, or when your travelling.
Hori make quality Nintendo accessories, so i'd be tempted to look at something by them: https://www.amazon.co.uk/Screen-protector-Nintendo-DS-lite/dp/B000EN2B1Y