OK- ready for some sacrilege? Pour some liquid dishwashing detergent down the bell of the horn followed by a forceful blast of water from your faucet, while wiggling the valves. Continue until only clear water is running through your horn. Turn horn around and blow forcefully into the lead pipe through your horn and out the bell to clear it of water. Wipe bell and horn dry. Put horn on stand and let inside dry thoroughly. Squeeze oil into the lead pipe and blow it through the horn. Basta!
You write that your horn is otherwise clean and that you don't want to go to a lot of trouble cleaning the valves etc. The above will just take a few moments so you're not put out any time. If it works, great and it's done what you want it to. If not, now you know that you have to do more work on it but you haven't already done it unnecessarily.