[Prudence]

Copyright protects an assortment of rights, including the right of distribution. Whether you're selling it or giving it away - distributing is distributing. (And since you're presumably giving these away in the hopes of drumming up future business, there's still a commercial aspect to the distribution.)

As far as privately-created renditions of the song are concerned - music is a special category in that songs have two sets of copyright. A particular performance has one copyright, and the underlying composition has another. You would still need permission to use the underlying composition. You would get that permission from BMI or some such licensing entity. But, it might not be too expensive. I have no idea what they would charge you, but it might be worth asking.