Can my cartilage be softened and nose nostrils less visible?

Based on your photos, you would be a great candidate for rhinoplasty. Your bump can be taken down and your tip cartilage modified to look smoother. Your columella is a bit droopy which gives you the extra nostril show. This can be lifted up at the same time without further rotating the nose. The key is to find a rhinoplasty expert that is comfortable with all of these things.

While it's important to keep in mind that no morphed photo is a guarantee, and your result will never be exactly what you see in a morph, I don't think that's an unreasonable result to expect. It shows a small dorsal hump reduction, tip refinement, and decreased columellar show. In my hands, this case isn't likely one that would require any fascia or cartilage from elsewhere (assuming your septum is intact!). You may even be a candidate for dorsal preservation. You hit the nail on the head that this is a finesse rhinoplasty, so find a surgeon with good training/experience and an aesthetic you like!