My sprouts are currently in their solo cups and are in coco coir and I am not currently feeding any nutes. Would you need to add very little nutes to your water since there aren't even trace nutrients in the coco?
Personally I'm a coco grower and I mix up a very weak feed solution to EC 0.5-0.8 then plant my seed in the coco.
Coco generally has a small amount of nutrients in it for buffering. Things calcium nitrate and magnesium nitrate. So there generally is a small amount to get going.