What is the ruling on touching one of the legs without being certain whether it is the ritually impure right leg or the left leg, and is it obligatory to wash both of them as a precautionary measure?

Initiating the removal of impurity from the body is obligatory or recommended. If there is an impurity on the foot, it is better to hasten its removal. As for the transfer of impurity to the hand, if both the hand and the foot are dry, then impurity does not transfer, even if the foot is impure. If one of them is wet, impurity is not considered to have transferred, because the default is that the hand remains pure.