You shouldn't have to replace the whole wire. Take the connector that was on the wire and try to find a new one at an auto store. Strip the end of the wire and crimp or solder the new connector onto it, then connect it back to the horn.
You might even get away with reusing the original connector, if you can reconnect the wire to it.
If the wire is now not long enough to reach, it's a simple matter to splice a little piece of wire onto the end, using a crimped sleeve connector, or use a soldered 'western union splice', covered with shrink wrap.
If any of this sounds strange to you, remember YouTube is your friend!