I have tried both and I don't find any difference is the final result.
If you dye first, then it's more difficult in the making stage because you have to prepare everything before final dye and stitch, but it's easier to dye.
If you dye at the end, it's easier to make the whole sheath first but it's more difficult to dye because of all the corners and hidden joins.
The only time you need to dye first is when you want the stitches to be white.
singteck
you need to show the result Richard