What is the ruling on washing the private parts from very little pre-seminal fluid with water without using the hand?

The private parts must be washed from madhy (pre-seminal fluid), whether it is a little or a lot, because the Messenger of Allah, peace and blessings be upon him, said: "He should wash his male organ and perform ablution." The washing is done by pouring water over the place of impurity and removing its trace. One must use the hand if purity is not achieved except with it. However, if the impurity is removed by the force of flowing water without using the hand, it appears that this is sufficient, especially if the madhy is wet.