Radio Shack makes a fairly small relay with 20 Amp rating on the contacts that would work well
Run a fairly heavy duty (14 gauge) wire from the battery to one of the relay contacts and then from the other contact to the horn. The two original wires can be connected to the relay coil to operate it. You'll probably need to run a ground wire from the frame or forks to one of the contacts on the horn and the other horn contact will be fed by the wire from the relay.
The coil consumes a low current and the higher horn current will be switched by the relay.
The Radio Shack relay has a mounting tab that will probably fit readily on some mounting bolt near the horns.