EDIT: FWIW, I think most bike paths are a travesty. You're better off out in the traffic where people can at least see you. Make them choose to run you over.
Britain: cycling injuries go down as cycling goes up: http://www.guardian.co.uk/environment/ethicallivingblog/2009...
New York: cycling injuries go down as cycling goes up: http://transalt.org/files/newsroom/streetbeat/2009/June/0604... http://transalt.org/files/campaigns/bike/images/ridership_gr...
It's also true that cycling goes down when people are worried about safety. Helmet laws and a focus on danger reduce cycling, which in turn increases injuries: http://www.thestar.com/news/gta/article/641641
Maybe me wearing a helmet increases the perception of danger, but hell, it's dangerous out there. Decreasing my immediate odds for safety is not worth some perceived future gains that I'm not even sure exist.
http://www.cyclehelmets.org/1019.html
"Many people who wear helmets can relate their experience of a crash which leads them to believe that a helmet 'saved their life'. This is a very common experience - very much more common, in fact, than the actual number of life-threatening injuries suffered by bare-headed cyclists. Yet there is no evidence that helmets save lives or prevent serious injury at all across cyclists as a whole"
The PDF linked at the bottom is good too, it's written by a guy that runs a cycle helmet testing lab.
http://www.cyclehelmets.org/papers/c2023.pdf
It's an in-depth piece and I don't want to do it an injustice by over-summarizing but here's my take: helmets by design and because of basic physical limits on their size are good for when you fall off a bike onto a flat surface at low speed, not for collisions, certainly not getting hit by speeding cars. Therefore they make a lot of sense for children learning to cycle or others prone to falling off, and much less sense for average cyclists.
What you're proposing is counter-intuitive to most people's everyday experience, ie. wearing protection is safer than not wearing it. Sorry, but if you really want to convince people you are going to need more than data, because the other side will have their own stats - and crying mothers and all that jazz.