You could try replacing each cars Horn.wav with something Silent... I'm fairly certain the game requires cars to have Horns to begin with, so you wouldn't just be able to delete them and be done, they'd become broken assets, but you could replace them.
If you have TS12 (IDK about the other versions) you can simply Disable cars in the Edit Route menu. Apply Static Cars as desired and call it good. TONS of route creators have done that in recent years (Though sometimes I think its a cop out for fighting with Road/YARN Assets, I think this is mostly a resource saving tool).
Falcus