It would be interesting to read if there were issued instructions detailing the cleaning procedure at the time. Or even pictures, dare I hope. I would assume their procedure would be similar to what I do.
I've taken enough Chem requirements to know nothing dissolves salts like water does. Salts don't form, it is a component of the primers and is left as residue after firing. The salt is hydrophobic and the moisture it absorbs and hold against steel is what causes the corrosive reaction. Water fit for cleaning a gun can be found almost anywhere so I assume the washing of salts would first be water.
Solvents (as would be used on guns) displace water. Think WD40 where the WD stands for Water Displacement. Next step would be displace moisture and scrub with solvent. Lastly apply the protecting oil.
I would doubt they would be hauling chemicals unnecessarily in wartime, and the half oiler bottle isn't really enough to do the salt removing - at least not more than once.
All just speculation on my part. Again, I'd love to find out what the Red Army training manual said at the time.