I have done this repair several times over the years and if you want to take it one more step you can hot dipped the door frames once repaired. It gets rid of the rust issue forever. I would suggest you remove the skins completely before you cut , weld and repair the door frame. I have seen people destroy the outer skin while trying to repair the frame and have to replace that as well
You can remove the skin with a small pry bar. You will also need to drill out a few pop rivets. They are a 3/16 blind aluminum pop rivet with an aluminum mandrel and are available at McMaster Carr. Seaming pliers do a good job of straightening out the lip. You don't need to glue the skin to the frame but I like to use little brush-able seam sealer to attach the frame to the skin. IMO it keeps the door from rattling. To re-install the skin, Use a small block of oak and a rubber mallet. Lay the door on a solid table or bench and use the mallet and wood block to bend over the lip. Pretty straight forward and easy repair. You will damage the paint. It's impossible not to but if you are careful you can limit it to the edge.
While you have the door card off, you may want to consider installing a piece of Dynamat or McMaster Carr insulation matting to the inside of the the door skin. It will really quiet the truck down.
All the best with the repair.