I'm unable to get rice noodles right now but I've never used egg noodles before. What is the difference in how I should cook it?
Usually, you would just soak the rice noodles in hot or boiled water for a minute/couple of minutes according to the packaging and then mix them in the with other cooked ingredients.
With egg noodles, you should cook them until al dente according to the package instructions and then add them in when you would the rice noodles according to the Pad Thai recipe instructions. Most likely, you'll boil them in water for a few minutes, drain them and then add them to the stir fry pan.
You'll probably get a lo mein-like dish with Pad Thai flavoring.
Here is a recipe that uses fresh egg noodles for a Pad Thai dish.