The "corrosive" term is misleading. The offending substance in a "corrosive" primer is potassium chloride (potassium salt, very similar to table salt.) It readily absorbs moisture, and when it does, it invites corrosion.
Potassium salt is water soluble. Water will remove it easily. Soap makes the water more effective at removing it. (Windex has soap in it.) Dish soap works just fine.
Soooooo, after you shoot, just swab the bore good with a water/soap solution, followed by the usual bore cleaner of your choice, and some good firearms oil.
Unless you have a pierced primer caused by a misadjusted firing pin, that crud won't be anywhere in the rifle except the chamber and the bore.
Think about this:
Russian or Soviet 7.62x54r ammunition has always been "corrosive". It's all that the Mosin Nagant rifles have ever fired. These rifles have survived quite well for up to a hundred and twenty years and dozens of wars.
Those Mosins are a lot of fun to shoot. Big boom, big muzzle flash, big kick. Lovable!