stick welding old thin header tubes?

If you can place a piece of copper or aluminum directly behind what your trying to weld. Steel will not stick to either of those two metals and the backing weld holds the puddle in place until it can harden. A old trick that works great on sheet metal also.
Regardless you can't weld rust.

X2! I use copper water pipe. You can bend it to desired shape and flatten it at the end and hold it with the ground clamp of the welder.
Or you can braze it with a torch and use a coathanger!