I would look at what requests youtube-dl sends and replicate that. youtube-dl itself has an option to output all the data it scrapes as JSON, but if you don't want it as external dependency, that's out.

jwz maintains youtubedown, which you can look at to find what/how it scrapes the information. At one time I looked at converting that to a module to make it accessible from other programs, but that wasn't as easy as I thought either.