It's been my experience that oxidized .22 bullets and hard, dry lube need to be cleaned off individually and relubricated by hand. Beeswax works well because it warms up at body temperature and will reharden. But other lubes will also work, even Alox I suppose. Another suggestion for a possible lube may be a product containing lanolin such as Saddle Soap.
The powder won't be affected by an external application and loaded rimfire ammunition really shouldn't be heated up. Just go slow and take as much time as necessary to complete the entire batch.
Here's another similar thread and my response: