Can I Elevate my Tip to Disguise my Hump Without Dorsal Rasping?

I think the better way to improve your profile is to build up the bridge of your nose in the area called the radix.  This is the portion of your bridge above your hump.  This will give you a more feminine profile, while making your nose and face appear slightly more narrow.  Removing the hump will make your nose appear wider.  Rotating the tip will not have a significant effect on the appearance of the hump. 

In my opinion, you do need something to stabilize the tip.  This usually is done with a columellar strut, but can be accomplished with other techniques as well (ie the septal tongue-in-groove maneuver).  You are right that by first projecting your tip, the amount of reduction of your bridge will be less.  You have basically a "pseudohump" caused by a low radix (the starting point of the nose) and an underprojected tip.  The key to having a long-lasting and pleasing result for your nose is stable tip projection.

The approach to rhinoplasty is very individualized.  In general, I agree with Dr. Lee that your tip should be augmented with cartilage tip graft in addition to slight elevation of the tip.  Upward tip rotation, in my hands, is predictably accomplished by trimming lower lateral cartilages, caudal septum, tip graft, and potentially, suturing to septum.  Lowering the dorsum and/or augmenting the radix (top of the nose) won't really add much down time, although it may add some cost, but will improve your overall result considerably.  Treating the tip alone will NOT camouflage the dorsal bump.  

You are young and beautiful.  If the nose bothers you, and the dorsal hump bothers you at all, I would treat the dorsum as well.  It will be worth it many times over in the long run, provided your result is good.