Here's another relay you could use:
3 - 60 seconds, 12V
To answer your question, a completely separate line from the timed output of the relay to the horn will not interfere with the original line from the horn button. They will be 2 independent lines going to the same device except that one is timed and the other is instant from the horn button.
Now if you want to drive the horn and the lights with the timed relay, you need a way to isolate the two so that turning on the lights will not activate the horn. To do this, you could run the timed output to the horn and to a another relay. The second relay will provide 12V to the headlights when activated by the timed relay but will also keep the horn and lights isolated when the timed relay is inactive.