Recipes for white chocolate style cake (or ice cream/truffle/...) coatings (the snappy kind, not soft frostings) tend to rely on cocoa butter, shortening, sugar... and milk powder as a filler. Soymilk powders are not available everywhere and make an unreliable substitute due to very brand dependent additives and properties. What can be used as a reliable, non-dairy filler?
Honestly, I would look at almond flour.
what milk powder gives to the recipe is proteins, sugars, and fats - all of which are present in nuts. This is also why almond milk is totally a thing, there are a lot of similarities.
Two major differences are, there will be an almond flavor instead of a (milder, more "neutral") milky flavor. And, almond milk has some of the almond solids removed, using almond flour is therefore "grittier" (not quite sure how else to put it) that using milk powder. A true substitute would be extracting and dehydrating almondmilk, so those extra solids aren't present. But, honestly that's a lot of work, and almond flour will probably work well enough - though you might revisit if you're using a lot, or if you think it's worth the extra work.
Of course, any other nut flours will also work, and even soy flour or coconut flour (both of whose precedents can be made into -milk) can be adapted. The extra flavors will be in the finished product, but they can be left as subtle, or celebrated, or something.