For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
References to Jesus' hands can be found in John 20: 20,25,27. The following verses come from the New KJV.
John 20:20 -20 When He had said this, He showed them His hands and His side. Then the disciples were glad when they saw the Lord.
John 20:25-The other disciples therefore said to him, “We have seen the Lord.”
So he said to them, “Unless I see in His hands the print of the nails, and put my finger into the print of the nails, and put my hand into His side, I will not believe.”
John 20:27-Then He said to Thomas, “Reach your finger here, and look at My hands; and reach your hand here, and put it into My side. Do not be unbelieving, but believing.”
Jesus told doubting Thomas, "Reach thither thy finger, and BEHOLD MY HANDS...John 20:27. Therefore, the nails were in His hands.
However, wrists would not contradict the use of 'hands' in greek. Cheir can include the wrist. In Luke 15:22 it's used for finger, in Acts 12:7 for wrists - so it could refer to any part of the hand entire, not just the palm. [And the hebrew term for 'hand' (yad) is actually different from the hebrew word for palm 'kaph'. (II Kings 9:35). Wrist falls under yad (Gen 24:22, Gen 38:28, Judg 15:13-14) as there is no word for wrist in hebrew. There is no word for wrist in greek either.
Where he was nailed is not of great importance save the prophecy that none of Jesus's bones would be broken (Psalm 34:20, Num 9:12, Ex 12:46, John 19:33-36). So, whether some spot in the wrist or palm, the important thing is that the placement of the nails did not break any of Jesus's bones.