You might contact Vince Warner at Colmwood Wheel Works in Hailsham, Sussex. He is encyclopedic about all things Sturmey Archer. He will have the correct axle and more than a few hints about the rebuild or quirks of the AB model, to help,you. It is worth the price to buy from him. He has supplied me with a 6 1/4" axle for a 60's vintage FW and the appropriate two-part indicator spindle for this particular application. He had the indicators manufactured to original SA spec ( probably better than the last few runs made by SA). He has parts, shifters and hardware for virtually anything Sturmey Archer.

https://colwoodwheelworks.co.uk/

Happy Hunting!