Yes the tining will prevent corrosion if applied well. I would still heat shrink over it. If you plan to simply solder into the existing speaker wire, then adding a short piece of silver wire to each end of the cap and then soldering to the existing speaker wire would not be worth the effort and not a good idea. Just use the copper leads to the internal speaker wire.
If you want to use the silver wire to connect directly to the tweeter, then it makes sense. Not sure if you are planing to rewire the tweeter crossover parts with your silver wire?
If you want to use the silver wire to connect directly to the tweeter, then it makes sense. Not sure if you are planing to rewire the tweeter crossover parts with your silver wire?