I tried most methods as found on the www. Some barrels would flash rust if cleaned with water some would not. Settled down to use Ballistol (I guess any soluble oil would do but this I had from before). B milk is 1 part Ballistol to 8 of cold water. Cleaning patches are soaked in B milk and pressed almost dry. I clean until most foulness is gone, never go mad. I dry with few patches of paper kitchen towel, sturdy one that do not disintegrate. I immediately follow with neat Ballistol patch, not milk patch. When out and about, without neat Ballistol, B bore butter patch would be the last one instead. B bore butter is ½ lard, ½ beeswax and few spoons of Ballistol to adjust for the season. I used WD40 few times, when pressed, no adverse effects found. But I do not trust WD40 for more than few days storage.
I would suggest you test any method suggested, like mine, on an old car pannel, that steel rusts like no other.
I tested alcohol, it evaporates and leaves the surface still wet, until water evaporates as well. Wet steel rusts far faster than dry steel. So you should dry it immediately, and grease it immediately. Stuff like Ballistol would soak away any water left behind dry patch and slow down rusting. But any BP friendly fat would be better than none.
Remember Neil Young: Rust Never Sleeps.
