In your other thread with the same question, I said I stapled a shower curtain liner in place and that it had worked for 5 years. I was afraid of using any sealant for fear of toxic fumes...
There's a plastic waterproof non-toxic plastic sealant called 'Contact'. I heard they work really well with wood and non-waterproof materials and is very easy to apply. Just make sure there aren't any sharp things or abrasive items that may cut/wear away the plastic.