I've always found this to be the most surpising thing that people outside the field don't know. For some reason people have the idea that 70% of dermatology is cosmetic (probably because of the sterotypes that are so common in medicine).
Not only is it possible to do no cosmetics as a dermatologist, it is COMMON. The vast majority of dermatologists do very little cosmetics (maybe 10% or less, for patient that come specifically requesting something). There are a few practices that do a lot, or have a person that specializes in doing cosmetics. Most dermatologists probably do 60% skin cancer/neoplasms, 25% inflammatory/autoimmune conditions, 10% infectious and only 5% cosmetic. There will be pletny of people you can refer to when your patients request botox or fillers.
I would argue that an average plastic surgeon does far more cosmetics than an average dermatologist, unless they specialize in reconstruction.