Pro2a,... I never came across a "bone dry weapon" ,.... I have a good idea what you are trying to relate, I just never came across one.
Also,... I have never come across a weapon with a " chalky surface ".
So, it is kinda hard for me to have a first hand experience recommendation for you.
But I will tell you what I would do
I have used a variation of Ed's Red cleaner and lubricant for well over a decade now, on ALL my weapons, for ALL my needs, from slight surface rust to bore cleaning and action lube! It has NEVER failed to give me the results I wanted. I have read that this formula can adversely effect some wood finishes, but I have NOT found that to be the case.
I mix up a gallon at a time, and it lasts me for YEARS!!
Here is one of the published formulas, for Ed's Red, just to save you a google

,...
CONTENTS: Ed's Red Bore Cleaner
1 part Dexron ATF, GM Spec. D-20265 or later.
1 part Kerosene - deodorized, K1
1 part Aliphatic Mineral Spirits
CAS #64741-49-9, or substitute "Stoddard Solvent", CAS #8052-41-3, or equivalent.
1 part Acetone, CAS #67-64-1.
(Optional 1 lb. of Lanolin, Anhydrous, USP per gallon, or OK to substitute Lanolin, Modified, Topical Lubricant, from the drug store)
I only mix up a quart each of the Dexron ATF, kerosine, mineral spirits and acetone,... not interested in the lanolin. The last batch I mixed up has been sitting on the shelf for 5 or 6 years now and it is as good as the first day I mixed it,... has never separated,... or changed in consistency, ONE BIT, from DAY ONE, to today!
I would break down the "bone dry weapon with chalky exterior" as much as I could, and let all sit in a jug of Ed's Red. Enough to be well above all parts, for a couple days.
That is what I would do,... but, not SEEING and TOUCHING exactly what you are talking about,... all I can do is give you this uneducated suggestion for your specific situation.
All the best!
P.S.,... if you do mix up a batch, and want to be cautious,... try scrubbing a small section of the surface with some and an old tooth brush. I have no doubts it will have a positive effect on your " bone dry condition ".