Even if you found a way to protect your image from being duplicated, who's to say an accomplished holographer or computer scientist doesn't create a close approximation of you?
Something that I don't think is entirely clear is if all holographic images hold the same value. Those made by extrapolation from archived images or freehanded from memory might not be as accurate or desirable as those made with holographic cameras. The same could be said of the difference between an image of a president made from others and one made from a sitting of that president. Tiron might easily created an adequate hologram by having a computer synthesize available images; he might just impost her likeness on a generic humanoid form. On the other hand, he might be seeking a level of detail that is otherwise impossible without direct observation and recording of Kira's form.
If any of that is the case, than it might be possible for the individual to control their image and prevent an accurate hologram from being produced. That doesn't mean that a picture of their face won't be superimposed on a sex doll.