Here is a snapshot for you.
http://www.nhl.com/stats/player?rep...1&aggregate=0&filter=gamesPlayed,gte,60&pos=D
63 RD played more than 60 games last year. 152 defenceman in total played more than 60 games. You can estimate from these numbers that only 41% of defenceman last year that took a regular shift shoot right.
You switch that to played in the NHL period, it is 119 RD and 306 total defenders, for a 38% RD and 62% LD. If you go back 10 years, there have been 325 RD seasons with 60+ games and 868 D seasons with 60+ games; which is around 37.5% RD.
The other thing to keep in mind, is that all things being equal, since there are less RD, the RD makes the team instead of the LD. For example, IIRC, in 2012-13 we played Potter 68 games, and Fistric only 25, but Fistric was a considerably better defenceman, who outpaced Potter in scoring, was more physical, and wasn't eating PP time like Potter was... but we played Potter. Or, Fayne played more than twice Oasterle and Reinhart, despite both players outplaying Fayne all year. So these numbers are skewed at least 5% towards RD's as well.
Most Canadians are Right handed Left shots; the idea being from the 60's that it is easier to learn power with your less dominant hand than it is to learn finesse required from stick handling. Truly, it is all kind of hogwash and doesn't matter either way because good training would get either hand there after thousands of hours regardless. Its just a grandfathered thing really, peoples parents did it that way and taught their kids that way, who taught their kids... Haha.