Is what you want the feature that Word calls a Page Border? That isn't built
into Excel. Help says to get that effect you do what you are doing now, select
the cells and apply a border to them.
If you have a graphics program, create a graphic that consists of a rectangle
with a colored border and transparent interior. Insert that as a picture in
the header or footer. I played arount with that a bit now, and it was
frustrating. I saved the 7.6 x 10.1 graphic with a 3 pt border just inside the
edges, in TIFF format, preserving transparency. I couldn't get all four sides
to print. Probably has to do with my margin settings and the size of the
graphic.
I wonder if the easiest route would be to set up a document in Word with the
border you want and no text, print several sheets with just that border, then
put the paper back in the printer and print your Excel sheet.