Will it be possible to use my own cdn instead Azure CDN to deliver media content?

Yes, you can use third party CDN providers with Azure Media Services. You simply stop your Media Services streaming endpoint, disable the Azure CDN, and start the streaming endpoint once again. Once running you can point your CDN to the Media Services streaming endpoint host name. The main difference will be that your clients will access your third party CDN endpoint host name whereas with the Media Services CDN enabled streaming endpoint the hostname stays the same whether or not the CDN is enabled.
FYI, content protection (DRM) licenses and keys are not delivered from the streaming endpoint. They are served from a key delivery server. For this reason the streaming endpoint configuration doesn't matter.