I've read a few sites explaining how to dry your noodles, and I know the store bought ones are not made with eggs. I tried experimenting with no-egg noodles though and they just came out too gummy. I've not seen any site explicitly saying it's ok to dry egg noodles. Raw egg is kind of a scary thing; I know they do end up cooked eventually, but in the meantime can they get all nasty so they make you sick and/or taste like ash?
My italian grandma does it, but says to really make sure they dry out.
You can dry them out and then freeze them, if it makes you feel any less hesitant.
I have to say. Yes, it's safe as both Chinese and Italian have been doing that for many years.
The only thing I would say is How are you going to dry your noodles? Usually drying noodles require some device(s) or natural sunlight.
In my opinion, I will make sure the noodles are still fresh and I will dry noodles under the sun. I may leave it under the sun for a longer time which I will make sure all of the moisture in the noodles go away, otherwise, it can go off easily.