Im playing a piece that goes from high C to D, too. I was playing the regular fingerings (and its quite hard...) so Ive just been using the trill key and it sounds better, you just have to watch to make sure you don't start playing sharp (which is also a pain but I have a solo contest coming up and I need it to sound decent )Ill ask my oboe teacher tomorrow
I played Mozart's oboe quartet for an audition and had to go quickly from a high d to high c. I just used the regular fingerings where I could, but I also used the trill key a few times. I would say to maybe try practicing going from c to d slowly, and then increase the speed. If you needed to, try figuring out how to make it sound good with the trill key.