I agree with the other surgeons. Thick, oily skin is not likely to result in a very refined tip. However, there are options and all hope is not lost.
Depending on your skin, during surgery the under surface can be thinnned out or "de-fatted."
Structural grafting and suture techniques also are often used in thicker skinned patients to give them very nice improvements in their tip.
Computer imaging to see what exactly is realistic as far as outcome is paramount. You have to see what is possible before you go through any surgery. If you like what you see then you can consider proceeding but if you think the imaged picture's tip is just not as narrow or refined as you had hoped, well then you don't have to go through surgery.
Now for the big one: Accutane, which is a very serious medicine used for severe cystic or nodular acne can usually thin out the skin and reduce the oil glands very nicely! The problem is that the medicine itself can have very serious side effects and no one in the U.S. will prescribe it for the purpose of getting a more refined nasal tip but it is used in other parts of the world for this purpose. I would not recommend you doing it but it is an option you should be aware of.
The important thing is to know that the old methods of cartilage excision to narrow the tip do not work on patients with thick oily skin and usually end up making the tip more amorphous and round in the long term.