I would think there would be two ways to do black legion cult troops.
first: black legion with cult troop details, shoulder pads in proper colors, skulls for Khorne, pustules for Nurgle, flayed skin for Slaanesh and. . . mutations for Tzeentch this suggest a more cohesive unified whole.
Alternately: you could put more weight on the crusade part, lots of different hertics workin together and so paint the Cult troops up with there proper cult colors, but with only slight nods to Black Legion, like black legion shoulder pads, banners, ectra. Contry to the above this gives a more disparate look, less a unified whole and more a bunch of guys from different sides coming together for singular purpose.
Which one you pick depends on how strong you picture your commander, does he command the direct loyalty of the cult troops and IS there warmaster, or do the cult troops have there own leaders that he has to work with, but can't boss around.