Can a tip plasty avoid any possible breathing issues that can come from a full cosmetic rhinoplasty?

Hello and thank you for your question. A procedure limited to just the tip of the nose could definitely address your concerns, and is probably less likely to cause breathing issues when compared to a full rhinoplasty. That being said, breathing issues after tip-plasty still can occur, so it is good to be aware of this possible risk. Rhinoplasty in general is not a skin procedure. The surgery addresses the bone and cartilage beneath the skin, and the skin simply drapes over the new framework that was created. The thickness of the skin can limit the amount of change that is able to be made.

Short answer is yes- the risk of complications, in general, should be less with a tip plasty.
A more complete answer, however, is that a properly done rhinoplasty or septorhinoplasty should not cause any breathing issues. If anything, your breathing should improve after swelling has resolved. There are two main 'valves' that control airflow within the nose. The external valve (which is basically located at the nostril rim and columella) could be affected even during a tip plasty. The internal valve is further up within the nose and should not be affected by a tip plasty, but could be during a more extensive rhinoplasty.
A drooping tip can be corrected with a tip plasty (with grafts to support the tip), but an overall facial and nasal aesthetic assessment really is needed to determine what is best. Thick skin often increases swelling and recovery time, but otherwise can have just as nice a result as with thinner skin.
Hope this helps!