Cedar is a no-no anyway because it's too aromatic for birds. Can you use aspen? It's considered to be the best bedding for birds since it doesn't contain aromatic oils, which probably also means that it's the least likely to cause allergic reactions.
If aspen is feasible, you want a brand that isn't full of dust - this benefits both the birds and the humans. Kaytee is a nice clean brand.
If you wanted to test the aspen, you could buy a very small package but not put it in the nest until you're sure it's OK to have in the house. Your husband could try it out in whatever way seems safest and most appropriate, for example starting out with the aspen in a distant room and gradually moving it closer.
It can be used as a last resort bedding. Some of the draw backs are the sharp ends of the pieces can puncture delicate skin of small babies. Also if it gets damp it can get moldy and lead to respiratory problems. how it gets damp is the parents wetting their feathers to bring moisture to add humidity in the box for the eggs and/or young chicks.