I have never used that particular sealer, but since it states non toxic then it should be safe.
We have always used the polyurethane, letting it off gas, etc, without any trouble or issues either.
Which wood did you choose?
I made the enclosure out of maple and birch.I bought a 4x8 sheet which I thought was birch however it was mislabeled and turned out to be maple. The back is birch as well as the nailer pieces
All hard drying sealers are non-toxic ONCE CURED. The differences are how long a particular product takes to cure and how hard/durable the final finish is. Typically, though not always, the oil based finishes are more durable then water based finishes but emit more fumes and take longer to cure (dry to the point they no longer emit toxic fumes)
To answer your question specifically, Polycrylic sealer from home depot is water based and non-toxic once cured. Its essentially plastic once dry. You can also use a standard polyurethane, but it will take WEEKS to cure.
For polycrylic I historically have waited at least 1 week after initial application for the product to fully cure, and that's with the sealed item being placed in a warmer area with good ventilation. For polyurethane I'd wait at least 1 month for the product to fully cure with no continued off-gassing/fumes. Once these products are fully cured they are non-toxic, UV stable, and offer a decent level of water resistance.
The products to avoid are non-drying products, such as oil finishes.