Thanks to all. Yes, obviously, the lids would breathe. The question
is, would desiccant be able to take care of relatively little moisture
that enters the boxes during said "breathing".

That stuff is kind of valuable on a per tool basis. I placed moisture
measuring pieces of paper that came with desiccant, in the boxes, I
will see how they change.

Spraying them all with oil, is not very practicable.

I may clean up the shed a little and move them into the shed, and
maybe add some safe heating to them.

i