It's very understandable that your ball speed will be lower with your non-dominant hand. I have tried to throw a ball left handed before for laughs--it wasn't pretty. Not only was I uncoordinated, I just simply didn't have the same strength in my other arm. However, arm strength doesn't have as much to do with ball speed as your form in many cases. Other than of course matching up your equipment to your lower speed, one of your best bets may be to practice as much as possible to build up your coordination and strength with your right arm, plus working on developing a form that lets you increase your ball speed.
I am not a strong guy by any stretch of the imagination, but I still generally have a 17mph ball speed, sometimes 18mph, throwing a 15 pound ball. I generate my speed with my relatively long legs and with a free arm swing. I stand at the back dots and I use my long legs to take longer steps (I only have a 4 step approach, though being 6'0" helps that some). Combine that with an armswing that lets gravity do its thing, and I don't have to put much muscle into it.