You could use a piece of poster board. There is this stuff at Wal-Mart and similar stores which are kind of like putty that you can hang posters and such on walls and is removable. I don't know if it would work on corkboard, but you could give it a try. Listen to your husband on this one. Like, it can let the air out of the little person, then flip closed when he tries to breath in.
Tacks are terribly dangerous.
As an alternative, how about that stuff that is like clay. You pull a piece of it off, and it acts like clay. Or maybe some double sided tape. You could save a little money here, instead of buying a cork board, maybe a nice large, decorated poster board. Hope you find something that works.