Just checked the FAQ.
MOVE
Some effects allow players to move cards or tokens.
• When something moves, it cannot move to its same (current) placement. If there is no valid destination for a move, the move cannot resolve.
• When damage is moved to a new character, it ignores shields and the character is not considered to have taken damage.
As the damage is not taken or dealt, Dooku cannot use shields.
I consider this matter resolved.