You could just get some old cigar boxes, break them up and glue them to the walls of the fridge if you want some wood. Most people use Aquarium silicone/sealant for fixing air gaps and should be fine to hold the wood to the walls of the fridge. You could also use velcro to attach the wood with no odor. Here's a link to other woods you should consider for protective reasons.

http://www.humidor-guide.com/humidor...ar-in-humidors