I tried to order the black rubber and alligator strap with red stitching, FC6400, from LVMH service division in New Jersey for my CAR2A1Z while it was being serviced but was told that strap was not available for purchase for my Heuer 01 as it was exclusive to the Manchester United Heuer 01. They did however kindly offer to sell me the either the black, red or white rubber straps as well as the steel bracelet. This was in May 2017. It looks like the brown calfskin may also be offered on the original Heuer 01 from the recent TAG Heuer picture.
If you can get someone to go the extra mile for you and make an exception and order the strap you want, that is terrific. I am not being critical but I do wish that you could order any strap you want for a Heuer 01/02, etc. as long as it fits, much like you can with the Connected Modular 45 watches.