I think the walking is fine, but I have a concern about holding the weights for lengths of time.

Since you had carpal tunnel already, which is usually due to RSI (repetitive strain) -( I have had lots of PT for various RSIs myself..)- I wouldn't do any constant holding/gripping = constant tension.
Unless your carpal tunnel is not an issue at all anymore, I don't know how long ago your surgery was.

Just my thoughts, I would focus on gentle moving and stretching of the hands & fingers while on the treadmill.