Is it permissible for the wife to give charity from her husband's money that he gave her to dispose of without his knowledge, knowing that he would approve of it?

There is no harm in a wife giving charity from her husband's money if she knows he approves, and this should be with a small amount that the husband would be pleased with. As for a large amount, it depends on his permission. This is supported by what was narrated from Aisha and Asma, may Allah be pleased with them. The permission can be explicit or implicit, based on common practice and the husband's known consent.