I've recently found a procedure where you mix your carbonyl compound, methanol, 5 equivalents ammonium acetate and something less than 1 equivalent sodium cyanoborohydride, and heat to reflux under dry inert atmosphere.
It works well for my ketone; not sure about aldehydes, but I guess you can try on a small scale and see how it goes.
If you really can't use any hydroxylated solvents, you might try with a solution of ammonia in dioxane (very expensive though).
However, I think your product can't really be *that* sensitive to water, because already the first step of reductive amination produces water.
Using benzyl or PMB... yes, it has been done, but honestly, it's a pain in the ****