Yea, all you really need to work on is knowing a scale or two and playing it fast in various positions on the fret board, shredding is fairly simple. Most shredders stick to this traditional form or just running scales in the particular key of whatever song they are soloing in.
I'd advise against it except for learning how to shred. when you start making **** up try and get more cretive with whatever you are "shredding" on the guitar.

My first tip would be throw out what you know of trem picking since it makes up like 1% of all true shredding.
Accurate rhythm when playing lead is essential to playing clean and well sound really good, not just good. Though there are times where cutting the perfect rhythm corner can be done.

Second whatever you do start slow at learning to play lead fast, build speed naturally, that way you don't just train your fingers to move quickly and efficiently, but have a more balanced ability to go slow and fast.

One of the most common training exercises for building speed, accuracy and dexterity is the ole:

|------------1-2-3-4-
|1-2-3-4---------

up and down the fret board over and over again, just go down all the strings and come back up all the strings. It's best to do this with some sort of metranome so that you can accurately time everything. I'd say start slow at at least 80 tempo. You might find this absurd and too slow to play at for a while, but then you can start playing 16th note tripplets and find out that it gets a little harder or 32nd notes at that speed.

If you would like me to send you some exercises in tab format that i have run across over the time i've spent learning to shred just e-mail me at graphics_ninja@yahoo.com

hope this helps you some.