Since you'll be making them with hard, grating cheese, it's more likely that your cheese straws will soften up before they go bad. Refresh them in the oven to recrisp, or freeze them before or after baking. I wouldn't keep them at room temperature for longer than 5 days. I think the best thing to do is make a lot and only bake off what you need, freezing the rest to bake later. Frozen puff pastry cheese straws will be fine in the freezer for a couple of months.