Know any YouTubers who tend to play small, browser-based games who might be interested? Is this even standard practice?
You can find a list of Let's Play-ers here
There are descriptions of the types of games they generally play, so you can target only those who you think would play your game. Look for those that play Flash or Indie games rather than Browser games, just use Ctrl+F to search for them.
Even if it's not standard practice, it's better to be pro-active about getting your game out there than hope people stumble across it.
Just be friendly, informative and to the point when contacting them. Make sure you include a link to your game and a few screenshots or a video you've made, so they can see the game without having to search for it. Something like:
[quote:1omwgtgh]Hey [let's player],
I'm an indie dev and I was hoping you'd be interested in doing a Let's Play video about my new game [Game Name] [link to game]
It's a [platform/genre] game about [this awesome thing] and [that awesome thing], where you have to [do this awesome thing].
[screenshot 1][screenshot 2][screenshot 3]
Feel free to contact me if you want to discuss anything.
I look forward to hearing from you and seeing your video.
[link to website]
You can use a similar format when contacting games websites for reviews.
Anyway, I hope that helps.