Will shaving down the dorsal hump affect a drooping tip?

I don’t believe the work done on the nasal bridge will positively affect the tip. Your surgeon will need to refine the tip directly to achieve an optimal result. Keep in mind that rhinoplasty is one of the most complex of all plastic surgery procedures. The skill, experience and training of your surgeon cannot be overstated. Make sure you choose a board-certified facial plastic surgeon who has successfully performed many rhinoplasties to ensure you get the best possible results. 

Thank you for your question regarding shaving down the dorsal of the nose and the eventual shape of the tip. In my opinion, I would leave it up to the plastic surgeon. It is possible that shaving down the dorsum of the nose will rotate the nasal tip. However, I think in your case, you will also need nasal tip work.  Therefore, I would go into surgery with the understanding with your plastic surgeon that if just the dorsal work doesn't work, you may need nasal tip work. Your nasal tip work might entail resecting some of the cartilage and reconstructing the tip of the nose. Thank you for your question regarding shaving the dorsum of the nose. 

The tip of the nose does not come up or stop drooping when a bump is shaved down. In fact shaving the bump as an isolated procedure tends to make the nose *look* longer, as if the tip had drooped more. Elevating the tip, as in the woman in the short video that I posted with this answer, usually requires complicated work on the tip cartilages.Did the surgeon show you morphs of his anticipated result, so you know exactly what he's picturing for your nose?
How *much* to elevate the tip, or lower a bump, or make other necessary changes? We figure that out with morphs, well before surgery. I'd love for you to see some excellent professionally-designed morphs of what could possibly be done with your nose. Morphs could also help you identify what's bothering you, and help you set a goal for the rhinoplasty that's accurate for your tastes. Profile and three-quarter views would be particularly important in morphing your nose. (Side note: in my opinion, morphs should always be done by the surgeon, or he should direct an assistant as she makes the morphs. Morphs should be made with a constant eye to what actually *can* be done in surgery, for that particular nose, and only the surgeon has that information and judgment. Another aside: I also recommend that you not show morphs made by one surgeon to a different surgeon. If a surgeon makes his *own* morphs, you get to see whether he understands the important issues of your nose, and how your nose should be changed. But if you show the surgeon someone else's morphs, and he says "Of course I can make your nose look like that," then you don't really know if he fully understands, or even recognizes, the important changes shown in those morphs. And you don't know if he can make those changes during surgery.)
Remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, and skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And it also discusses how to take photos that are best for online evaluations.
A long nose with a bump on the bridge is also a perfect example of why computer imaging by the operating surgeon is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?