Even that your question was posted a month ago - I still hope my advice will help.
My career has two faces, Stage Manager and Fight Director.
(artistic director of Scuola Brancaleoni
www.scuolabrancaleoni.com).
A fight Captain is normaly being picked by the F.D.
It is normaly the one who knows, best, the choreography.
The main point of having a Fight Captain is to make sure the fight is being done SAFE, (when the F.D is away - after he or she are done with the choreography).
This way the production will not face legal problems...
The best thing would be to give the fight Captain 15 minutes "fight call" before each performance, to warm up and Run through the moves with the cast.
This is when you talk about actors - who are mainly fighters. (not leads).
Sometimes when the F.D. is busy they call another F.D. to check the Fight Scenes.
It is not only to be safe! but to make sure it will look good and not "tired".
In Europe, choosing a F.D. is the job of the production manager together with the F.D. (or the Director).
Fight Captains are not Fight Directors! they do not choreogaph - they keep the fight scene safe and in good shape.
If you have any more questions - or looking for good people to do this line of work, let me know
Swords Up,
Ran