Well, the safety is not supposed to be in two pieces, even though it was made that way. Unlike the Model 1911 safety, which is one piece, Colt made the Model 1903/08 safety in two pieces, the safety plate and the safety shaft, and swaged them together. As you found, they sometimes come apart.
A fix is possible if you choose to try it. You can support the right end of the safety shaft on something solid (like a vise), and then use a hammer to swage the left end. Just pound on it (not too hard) to tighten it up on the safety plate. That can usually be done with little damage to the gun and sometimes can't even be seen. As a last ditch, the shaft can be staked, but that looks like hell.
If you want to get a replacement, I recommend you not just remove the safety as it is also the hammer pin and getting the gun back together will be a bear. Buy the new safety if you can get it. Then, to replace it, follow this procedure.
Use the new safety to get the diameter of the safety shaft. Obtain or make a rod of that diameter or a tad smaller, long enough (5" or so) to hold onto. Brass will be best, but steel will do if necessary. Don't use plastic. Round the end slightly; putting a hollow in it is best, if you have a means of doing that.
Field strip the pistol and remove the grips so they don't get damaged. With the slide off and the hammer cocked, clamp the pistol grip in a soft jaw (leather is good) vise. Move the safety to the up (on) position. With your rod, carefully push the safety shaft out from the right side. Keep pressure on the left end so the rod follows the safety shaft, not allowing the hammer to get free. You should be able to do this with just hand pressure, but take it slow. Once the safety shaft is all the way out, the rod should come through and out the left side.
Install the new safety, pushing it in and pushing the rod out, again making sure you keep control. Once the shaft is in, make sure the safety is in the up position and its end should come through to the right side. You are done.
If the new safety won't engage or won't go in, it will have to be fitted, which means more work with that rod and trial and error stoning on the sear engagement surface at the rear of the safety cam. I would say take the gun to a gunsmith, but I have seen so many of those guns really buggered up by "gunsmiths" that I hate to suggest that.
Jim
