Starting a rigorous new workout program can be extremely daunting, especially if you plan to work with a trainer. If you are worried that you might not follow through with your commitment, pay your trainer the full amount up front. You will be less likely to skip workout sessions if you have already made a significant investment.
If any injury occurs with one arm, there is no reason to not work out the other arm. Doing this has been found to increase the non-exercising arm's strength by at least 10%. This is achieved because working out the one arm stimulates the muscle fibers in the other arm.