There is no "proper" way to do this, the drip rail "gutter" is the pinchweld that holds the edge of the roof together with the supporting structure. It's not just decoration.
However, If you really have your heart set on doing this, you'll want to do a few inches at a time, leaving most of the rail in place as support. Make sure your weld bead completely attaches all of the layers, or it'll crack, and give you structural problems.
Do you want to shave them because you like the look or because they are badly rusted? Unless there are large sections rusted through, smaller holes can be cleaned and filled using a MIG and a piece of flat copper underneath.
We have done it on three Mustangs. Two because of rust and one because I liked the look. Cut the drip rail off and than weld in a patch if there is rust or weld the two back together.
Rusty,
As always, showin' the "good stuff" and ALWAYS bringin' your "A" game. I so wish that I could afford to have you do my 68 Coupe. I'm certainly not implying that your prices are high, but the quality and attention to detail of the work that you show, surely can't be within the budget of mere mortals. Your stuff looks to be some of the best of the best.
Gene
Man, how do you guys stay in business working so cheap? Most bodyshops here are in the $75/hr and it goes up from there. Their work is nowhere near as nice as your either.