Is it possible to re-use a character armature and copy it to another character of the exact same body type and structure?

Yeah sure drag the symbol out onto the stage, right click on the clip and select Duplicate symbol and then right click on each of the body parts and duplicate them as well. Then click inside each symbol and replace the body parts.

IF you haven't placed the entire character inside it's own symbol you should do that as well. You can do that by click dragging all of the art and layers on the timeline, then right clicking it and selecting copy frames, then hit F8 on your keyboard which will bring up the Create symbol dialog box, name it, then go to your Library (Windows>Library) and double click on the symbol, then click the empty timeline and right click and select Paste frames. All of your art is now inside it's own symbol. Go back out onto the main stage and delete the layers on the timeline and then drag your symbol onto the stage.