First Production Egg Chair  

why not Fritz Hansen
they were/are the producer of your chairs..

Leather?
Have you considered leather?

.
Do you have any images? The really early ones I've seen photos of had a much sharper curve at the top and I'd like to see that again, have lost the original.

Maharam/Kvadrat Tonus
would be a great choice and was used on early Swan chairs, I know. Probably on Eggs, too. It is 10% Helanca (like Lycra) so it goes around curves very nicely. It's a soft, fuzzy textured wool, not as scratchy as M/K Hallingdal (which I also love, don't get me wrong). Comes in many colors, too. I believe the one I linked here is the one on the chairs at the famous Royal Hotel in Copenhagen.
You can order samples from Maharam yourself but you will need an account with them (and a tax ID) to buy from them directly.
http://www.maharam.com/products/tonus-by-kvadrat/colors/215

we redo those chair all the t...
we redo those chair all the time. The correct fabric is what Spanky showed you . or Tonus by Kvadat . That is what the factory uses.

you repolster egg chairs all the time....
I have a 1960 egg chair in desperate need of love.
I'm in a situation where I want to sell it after its redone.
Unfortunately I have twin babies and a wild house of two dogs, and I can only keep it under fort Knox for so long, what would you recomend for colour choice for resale, please and Thanks
Tuilp

LRF
Can you post images of some of the egg chairs that have been done in your shop? I'd be very interested in seeing the finished pieces.

that would be graet
It would be nice to see