Are you looking at wiring to an existing switch or adding a new switch. My suggestion is just add a new switch. With a horn you don't necessarily need a relay as a momentary SPST switch will work fine as long as the switch has a higher current rating than the horn. The only reason to add a relay is to control the high current associated with some horns with a small switch that can't handle high current. Based on a 12V battery source here's my recommendation for getting away from a relay:
Here's a basic switch circuit example. The light would be replaced by the horn. Direction of the SPST switch leads make do difference so just wire them up however rule of thumb is to place the switch off the negative side of the battery - between the battery's negative lead and the horn. By the looks of it the horn may not make a difference on its polarity either but if you do get it make sure. Total cost probably less than $20
https://www.amazon.com/Ulincos-Momentar ... ton+switch
https://www.amazon.com/uxcell-Universal ... s=12v+horn
Now if you absolutely want to add in a relay with a high current horn then here's the wiring diagram for one - you'll still want to use a momentary SPST switch. In terms of the diagram here just disregard the solenoid. Also the second lead of the horn would go to ground which isn't shown here.
If you're looking at reusing an existing switch in the PW's we need to know more about the switch and it's purpose - maybe even a photo. Is the switch a momentary switch? Is it a SPST, SPDT, DPDT, etc? Also I need clarification on the separate battery concept. Are you trying to us an existing switch (which means it has its own load and power source) to also drive a horn from a different power source? If the switch is a DPDT this would be easy but before I determine the circuit let me know if that's what you're trying to do?