First, let me tell you... I am a female so maybe it's not as bad to self-cath as it is for a male. Since my neobladder installation on 4/25/07 I have been dealing with hypercontinence and having to self-cath almost every time I pee. I was WIGGED OUT (just like you) about the whole procedure when the ostomy nurse made me sit through the self cath video, then made me try in the doctor's office. Not fun at all. Once I got home and was able to relax in my own bathroom with the cathether and the lube, it wasn't quite so bad. It only took me 2 or 3 tries during the day and by that night, I was self cathing in the dark in the middle of the night. Not nearly as awful as I had figured. No pain, very very very little discomfort.
Now that I know I will need to be self-cathing regularly (unless we can resolve the hypercontinence issue), I am using the medical supply company recommended by the ostomy nurse to try out all different kinds. There are a lot of different catheters available, all of which are far nicer and more comfortable than the red rubber one provided by the hospital. Some even come in "travel packs" with sterile water for the lubricant.
You'll do fine but you will be freaked out when they show you how to get the catheter in at the doctor's office or hospital. Just keep in mind that it's a lot less stressful when and if you have to perform the cathing at home. Hopefully with your neobladder you will not have to cath at all! That's the ideal result of the surgery... I am just an oddball. :
Good luck and trust me - you will be fine.