Are you saying you have trouble singing without vibrato, or turning down the vibrato? I think that's something you need to work on via singing exercises, a singing teacher or even just plain old willpower. Many people have the same problem, and not just singers. Guitarists are notorious for overdoing vibrato, I myself have to really concentrate in order to not overdo it when I'm playing. One of the things I always admired about Frank Zappa's guitar playing was his almost total lack of vibrato, it was all about the notes and the rhythm with him.
However, I get where you're coming from vocal wise....it's kind of leading toward an Alanis Morisette style. Actually a study of her vocal technique wouldn't be a bad thing....she uses a lot of vibrato like you, but it's a little slower and more controlled. Yours seems to be somewhere in between hers and Tiny Tim's...lol....no disrespect because Tiny Tim was an
awesome vocalist, but his musical style suited that very fast vibrato, whereas I think yours could maybe slow down a little.