You need two different antennas: one for shortwave, and one for the scanner
because of the difference in frequencies.

I would get something other than what Radio Shack offers for scanning. I had
a Radio Shack discone and wasn't impressed with its performance or its
durability. We get some ferocious storms here in the Fall and Winter. I had
a RS Discone, and come Spring when I could get to the antenna to check it
and do any maintanence, discovered several radials missing, and two actually
bent by the force of the wind . The parts of the antenna come loose fairly
easilly, and over time, the performance is degraded. Other people here can
recommend a much better antenna for your scanner.

Short wave nominally extends from about 1.7 Mhz up to 30.0 Mhz; Vhf starts
at 30 Mhz and extends upward and then you enter the UHF region and beyond in
the case of a scanner.

For a receiving antenna to perform satisfactorilly, you need it to be at
least 1/4 wavelength long, and 1/2 wave is even better, but at shortwave
frequencies, this length can get to be considerable, compared to scanner
frequencies, where an antenna only needs to be a few inches long. So the
actual antenna can't be the same for shortwave as for scanners.

Lastly, I don't know how tall your tower is going to be, but in order to get
the most from your scanner antenna, use the best quality of coaxial cable to
connect it to your receiver, and make sure the connection to the antenna is
sealed very well to prevent water from getting in, otherwise your effort
will be wasted, becauseI would stay away from any antenna amplifiers for
your scanner because it can produce ghosting and other undesireable
artifiacts, unless you are really on the fringes of reception.

HTH mm