Yes, you can put your plants into coco coir without hurting them.
When transplanting your plants make sure the soil is moist, take a butter knife and slide it along the edges of your pot to loosen it up. Then rest the plant stem between your fingers on top of your palm, turn your pot upside down to drop out the plant, root ball, and any dirt that may be attached. Put this beautiful clump into a similar sized hole in your new pot and you're good to go.
When transplanted smoothly, your plant will show minimal stress and should continue right on growing.