Was Arjuna left-handed in his warrior skills?
What about other great warriors of the epics like Karna, Bhishma, Drona, Rama and Laxmana?
Will left-handedness or right-handedness ever matter in acquiring warrior skills?
Arjuna was ambidextrous. Hence his name/title "Savyasachi". He was able to use both hands with equal facility. From Virata Parva
And since both of my hands are capable of drawing the Gandiva, I am known as Savyasachin among gods and men.
Use of the dominant hand will always matter in any physical or mechanical operation. In warfare, I would imagine ambidexterity gives the warrior a wider range of motion and hence target. It also allows the warrior to switch arms when one is tired, thereby minimizing the need for breaks unlike the average warrior.
Regardless of Arjuna's prowess, Rama is the greatest warrior and wielder of the bow of all times. Krishna says so in the vibhuti yoga of the Gita. There is and can be no parallel to Rama.
Of puriﬁers I am the wind, of the wielders of weapons I am Rāma, of ﬁshes I am the shark, and of ﬂowing rivers I am the Ganges.
Additionally, one can deduce that Rama was also ambidextrous because he is said to have carried quivers full of arrows on both his shoulders. See
The others you mention are all great warriors and perhaps superior to Arjuna but I do not recall mentions of their ambidexterity. The reason Arjuna prevailed even when facing warriors of Drona and Bhishma's caliber is having dharma and Krishna on his side.