Depends on the car. You could probably just drill out the spot welds and some can just be removed that way, others are part of the door frame opening structure. The other issue you WILL run into, is door gaps. You'd be suprised how much drip rails hide shitty door gaps. So, to fix that, you usually end up welding a piece of metal bent at a 90*, the whole way around the door to get a proper door gap. see picture...
another option, is just hammering the drip rails twards the roof, and welding them to the roof. see picture.
Any luck with your removing drip rails? I removed both mine on 67 Chevelle SS .... Where the top panel and door jamb met, they split open and separated, which I anticipated , and it TIG welded them back together a few inches at a time.
I removed the drip rails on my 61 Skylark. It is a tedious job, but not really all that hard. Cut about 1 - 2" at a time and tack weld as you go. The arear you have to weld may be very thin, so I chose to TIG weld mine. Of course once the rail is gone and all you have is tack welds, you have to jump around and weld a tiny bit at a time, until it's fully welded. I used a portaband to do 99% of the cutting. I will dig up a few pictures and post them. I know this is an old thread but maybe it will help someone serching in the future.