Run the solder over all the tape and the copper will turn silver(ish).
If you are not wrapping the foil around the edge of a piece of class you can buy stick on lead for windows that can be soldered, make sure you get the one for soldering. I think that it comes in 50m rolls and 2 or 3 widths.
The manufacturers do silvered copperfoil specifically for edging mirrors. This sounds near what you want. Try your local stained glass glass supplys for it.