I'm no speed demon but I do occasionally pass other riders. When I do I just wait until there's a ton of room then I move by with so much space between us that I don't have to announce. When this isn't possible I'll usually say something like "excuse me", give them time to turn around and see who said it, then they figure things out and move right. This requires slowing down to their speed which is a fate worse than death to some cyclists.
Perhaps something like "stay right" would be more effective than "on your left" because most folks hear "left" and move to the left.