I was reading Louis Armstrong’s account about a Jewish family he knew when he was a kid. He worked for them, and they loaned him money to buy his first cornet. Here’s the quote of interest:
(The whole thing is a great read, BTW)
What the heck is “insurance oil”? Oil sold by some insurance company? Oil sometimes used in arson to collect insurance? Google has nothing, and only says current horn cleaning uses lukewarm water, dishwashing liquid, and a snake.
It also appears here (do a “find” on “insurance”), as a preventative against mosquito breeding in cisterns and such.
Also appears in this Louisiana law archive (go to section 132 “Taxation”).
Unfortunately, no one seems to actually DEFINE it.
I’d be willing to bet that it was a brand name of that era. The oil itself is probably a light oil similar to current day 3-in-1.
HA! Re-reading this thread, and noting that the insurance oil “sterilized” the inside of the cornet, and that its use for the mosquito prevention was similar, I googled on “insurance oil” and “kerosene” and got a Dictionary of American Regional English Google Books cite.
Insurance oil is kerosene.
Sounds like it’s more or less the same thing as valve oil. Many years ago, I played trumpet & euphonium and went through quite a bit of the stuff; most of it had a definite kerosene odor.
jayjay’s link has this:
Which matches my second guess! 
I really did think it might be kerosene, but I thought, “Wouldn’t that be hard to get out of a horn?” Not all that hard, apparently.