Cool idea. Here in the UK a few of us still use traditional coin cabinets. The usual wood used to construct these is mahogany, because that's been found not to release any chemicals that will adversely affect the coins.
If you're using airtites I suspect that won't be an issue. And I'm sure you'll use properly seasoned wood. That will help keep any possible effects to a minimum.
And when you're done .... photos please!