Are there permissible ways and solutions to reduce the size of a large nose at the tip—other than cosmetic surgery, which you deem forbidden and consider the only solution—that do not violate Islam?

Summary of the answer: Means that involve cutting an organ for the purpose of beautification are not permissible, unless the organ is truly disfigured in an off-putting way that causes psychological or physical harm. As for means that do not involve cutting, but rather involve tightening the organ, it is more cautious to avoid them for the purpose of increasing beauty and attractiveness.