Good luck
Sounds like an interesting challenge!
You want to be able search the transcripts (and the titles and descriptions I suppose, but that's not the challenge) of a set of videos (eg a single channel)?
If you can't get access to the YouTube-generated transcripts - or for the ones they haven't created transcripts for:
Are you considering downloading / streaming the videos and running a voice recognition package against the audio? I guess not. Unless it's the only option.
Would you considering paying a few $$$ for a team of Indians to write transcripts?