Dave,
I have several years experience with CNCs. Matt is correct in the fact that you would need training. Either from a college, or a shop that is willing to take you on. In my case, it was a shop that was willing to train me. I started on manual mills in an engine machine shop along with some experience with the machining in the engine side. At that time, operators and people with experience in this area were almost non-existant. Starting in a CNC shop, I was a button pusher for several months. I spent alot of my own time learning as much as I could. In 2 years, I was programming CNC lathes by hand. Since then, I have ran CNC lathes, Mills, Wire EDM's and a stereo lithography machine. Now I work for a large PC, Printer manufacturer. My title has changed from a lowly machinist to Modelmaker/Toolmaker. The tools that I use daily are the exact tools that mechanical engineers use. (3D CAD, high end graphics workstations) Prototyping parts from drawing them in CAD to programming them in CAM then off to the mill.
Unfortunately, the manufacturing sector is dying/dead in the US. Alot of this is being offshored at break neck speeds. This is not to say that you could't get into this field at all. There is a high rate of unemployment in this field so it would/could be difficult.
Welding might be a better choice, however, it (at least in this state) is a low paying job. Specialty welding would be a better choice, but high stress.
Not too sure about any metal shop courses. The small shops in my area have been taken over by shops with CNC's. Most of these shops have manual machines to compliment the CNC's.
In the end, I will probably be able to retain my job in this field because of the level of experience that I have. Probably will have to sacrifice wage in the future.
HTH
Bill