I do a lot of dove productions. I do not recommend that you keep the birds in a typical box or body load for 40 minutes. There simply is not enough air.
You do not want air holes on body loads because the birds will start to peck at it. Hence, about 15+ minutes is really about max you want to wait if producing from the body.
The Collector's Workshop Dove of Life prop you referred to is nice, but again, not for concealing the dove(s) for 40 minutes.
I believe you will need to assemble/obtain your own carrying case, with air holes, to keep the birds for most of your talk. Perhaps this case can be concealed behind a stack of books or something germane to your talk. Then, say 5 minutes before your production ( so the kids won't connect your "move" to the later production) you can take the bird(s) out of the case and place them into your ultimate production vehicle....be it a book production, newspaper, etc., etc. Misdirection could be via asking for a volunteer, searching for and finding some rare book, item, etc. which was also behind the stack/ cover, etc. Anything to divert for ten seconds while you take the bird out of the case and place into your final load.
Obviously, this all could be made easier if you had an assistant, but your situation sans assistant is really quite managable.
Have a good show!