This is probably a stupid question, I am more of an Illustrator person, but what is the best way to add a 1 pixel border around the entire stage so it appears in swf?
Draw a rectangle (no fill) that is roughly the size of the stage using the line thickness you intend. Using the Properties panel set its width and height values to be one line thickness less than the stage width and height. Then adjust the rectangle's X and Y properties in the Properties panel to be 1/2 the line thickness.
The way I do this is let say the image is 250x250 what I do is make the size of the page in properties 252x252 change the background colour to what you want your border colour to be and when published you will have a 1px border around your image.