I have my wife's and my family all in one large database. As you get into your families you will find connection you had not idea existed. In my tree, I had always thought my parents were the first connection between the two family. Come to find out there was a connection about 15 years before my parents were married.
Just last night I realized to people in two different families were brother and sister, so by having them in one database it was easy to make the connection.
I don't think there is a way to share part of your database with your cousin. You can export part of you tree for you cousin. Or if you have an online tree, you can give him access to your tree.
While your cousin may not be interested in your wife's family, is there any reason you should not allow him access to your online tree? Personally even when give edit access to someone's online tree, I always give the information to them and let them add the information to their tree. If I add information to his tree, I may move his tree into a direction he did not want.
I don't have an online tree, but frequently share sub families with cousins from that subfamily. I have prepared four basic and extensive FTM books. Depending on the cousin's relationship I will send him one of the FTM Books or prepare a shorter book just for the portion of the family he is interested in. These FTM Books are not on paper, so when ever I print a book for someone it has the latest data in the database.