I could be wrong about this, but I think you'll need to use some sort of intelligent loadbalancer or reverse proxy of sorts.
I haven't worked with a related product in a while, but I used to do this constantly in my previous job by using Riverbed's ZXTM software. I'm not saying that that's the product you need to use (for one, it's quite expensive), but you will need something that can not only do URL reformatting, but also port forwarding.
I suppose there might be a way to reconfigure Sitescope itself to have the Tomcat component listen on port 80, but that might be very difficult to do since you'll have to then configure your webserver to listen on a port other than 80.
Changing the URL itself though should be as simple as adding a DNS entry on your DNS server if you have one.
EDIT: Just to expand on this a bit, I think a reverse proxy would suit your needs best. I'm not sure if there are any open source versions out there somewhere, but the idea of it is instead of connecting straight to Sitescope, you'll instead connect to a reverse proxy. The reverse proxy in turn will do the connecting to Sitescope and reformatting/ shortening the URL. Your reverse proxy can listen on port 80, which will remove the need for you to specify :8080 in the URL. You'll connect to the reverse proxy on port 80, but the reverse proxy will still connect to port 8080 on your Sitescope server.
Not sure if I explained it quite correctly, but hopefully you get the idea.
I am opening the firewall to access the Sitescope from public network. So that I want to use URL to open HP sitescope is: "HPSIS.solutionworks.com".
When we will use HPSIS.solutionworks.com in in web browser URL, It should open the Sitescope. I don't want to change the DNS name only needs to be configured as Tools level so that I can access the Sitescope which will use internally "http://server:port/sitescope"