Why didn't 10th Doctor cut and keep a body part after regeneration?

When 10th Doctor first regenerated after being shot by a Dalek, he kept his body same (using his old body part preserved by Captain Jack Harkness) because he had vanity issues at that time.

Just after regeneration, why didn't he cut his hand (or any other body part) again (which would have been repaired in regeneration phase) to use it next time (Vanity Issues)?