There are two types of copyrights. One is on the actual work, which is the music composition. The other is on the audio master recording. In order to have someone else record the music for you, it would still require licensing which can be expensive.
Instead I encourage you to find a music composer to write a piece of music and license it to you for your own use. If you do this, you will end up with a better music to fit your project because it will be written especially for your music.
You also run the risk of copyright infringement and YouTube will end up taking your video down.