Well, if you lose a tattoo in a morph you would lose a contact lens, not that thatever came up, but the morphing process doesn't do anything except heal old wounds. You don't remorph to have two arms where your legs should be and vice versa, nor do you end up with your t shirt on your legs, so the tattoo, not being a part of you yet being close to you should come along into Z space for the ride.
This does make me wonder, however, if they are able to morph with normal clothes on eventually, can they take that farther and morph with someone while holding hands. Like one person morphs and the other joins.