Can cutting the depressor septi muscle affect the shape of my nose? What can I do to stop my nose moving while I talk? (photo)

Hello and thank you for your question. Releasing the depressor nasi septi muscle can help prevent your tip from drooping with animation.  Based on your
photograph, you may also benefit from a tip refining rhinoplasty. Your surgeon can
accomplish this by trimming, suturing, and reshaping the cartilage in your
lower nose.  Make sure you specifically look at before and after
pictures of real patients who have had this surgery performed by your surgeon
and not just a computer animation system. The most important
aspect is to find a surgeon you are comfortable with. I recommend that you seek
consultation with a qualified board-certified plastic surgeon who can evaluate
you in person.
Best wishes and good luck.
Richard G. Reish, M.D.
Harvard-trained plastic surgeon

The best way to change the nasal tip droop is to have a surgical rhinoplasty. However as you are opposed to this the next option is to have botulinum toxin injected into the depressor septi muscle which is responsible for the dynamic droop of your nasal tip. There are also surgical options other than rhinoplasty to effect the nasal droop. Next step would be to find a qualified rhinoplasty specialist for a formal consult. Hope this is helpful. 

Hi!
You could try a small dose of Botox (or Dysport or Xeomin) to the depressor nasi septi muscle.  This would be a temporary and minimally invasive method to see if you like the way your nose and smile look when this muscle is inactivated. You may find that you love it, or you may find that it changes your smile in a way that bothers you, but regardless it will be temporary! I recommend that you go to someone with a lot of experience with Botox injections.
All the best,
Dr. Irvine