I did this on a 53 Ford truck that we chopped the top on. We used I think 1/4" round rod. I tach welded it as I went so I could bend it tightly around the top. Then I welded a litle at a time until it was solid all the way around(slowly obviously to prevent heat build up) then used a grinder to smooth it out. Our drip rail was pitted but most of it was solid so it stayed but was ground on pretty heavy, then mud over it.
I wouldn't advise cutting the drip rail off all at once the top could seperate I would think. I have pics of the top chop but none of the drip rail in there.