Praise be to Allaah.
It is narrated in a saheeh hadeeth that the Prophet (peace and blessings of Allaah be upon him) said: “None of you should touch his penis with his right hand when he is urinating, or wipe himself with his right hand after relieving oneself, or breathe into the vessel (from which he drinks).” (Narrated by Muslim, al-Tahaarah, 392)
Al-Nawawi said: The right hand is not to be used for any of those things for cleaning oneself after relieving oneself (i.e., either urinating or defecating).
On this basis, one has to use the left hand for removing najaasah (impurity), no matter how it is used, whether one uses the entire hand or part of it. The aim is to remove the najaasah from the body. The issue here is flexible; what matters is to avoid using the right hand in removing dirt. And Allaah knows best.
See also Question # 2532