If the Bible speaks relatively highly of the right hand, does this imply that the left hand is somehow weaker or that left-handedness is a sin? Not in the slightest! The fact that Scripture emphasizes the right hand over the left is simply a reflection of the reality that 85-90% of people are right-hand dominant. Since your dominant hand, arm, eye, or even foot is used more frequently and is most often physiologically stronger than its counterpart, it only makes sense that the right hand would be used as a poetic device to symbolize strength, honor, or privilege.
When does the Bible actually mention lefties?
In the few instances in which the Bible mentions left-handed people, they are certainly not described as weak or sinful, certainly no more so than the average righty. In Judges 3:15-21, you can read about Ehud, a judge of Israel and a mighty warrior, who was left-handed. Judges 20:16 also mentions 700 left-handed soldiers of the tribe of Benjamin who could “sling a stone at a hair and not miss," which certainly sounds like an honorable mention to me. First Chronicles 12:2 is believed to be about ambidextrous archers. Left-handedness is not a molehill that the Bible makes into a mountain, but on the odd occasion a lefty is mentioned, it is in a positive light.
Lastly, we can look to Matthew 20:21, in which the mother of apostles James and John asks of Jesus that her sons "may sit at your right and the other at your left in [his] kingdom." Neither man was considered less honorable, and Jesus replied that both the left and right positions were for God to give. It's just a matter of Jesus only having two hands and two sides at which they could sit!