Hi,
That sounds as though it will work fine then. You just have to remember to lift it back out before trying to slide the second glass door.
Since he won't be able to get to it you can use the small, self adhesive, rubber patches for fixing leaks in bike tyres to help you get a better grip on it to lift it out if you like.
Or drill a hole in it if you choose perspex.
Either way remember to make sure the edges aren't rough or sharp as he is liable to try quite hard to get into his usual hiding spot.
dr del