With regard to the water that goes beyond the site of the impurity when cleaning oneself after relieving oneself, if it is changed by the impurity then it is impure, but if it is not changed, then it is pure, whether it runs over the body or drips from it. What matters is whether it is changed. This is the view of Malik (may Allah have mercy on him).
Ibn al-Hajib (may Allah have mercy on him) said in Jami` al-Ummahat, p. 38: Water used for washing that is changed is impure, but that which is not changed is pure. End quote.
See: al-Mawsu`ah al-Fiqhiyyah, 29/99.
If you are certain that the water that drops has been changed by the madhiy or urine, you must wash off whatever of it has got onto your body, but if you are not certain, then you do not have to do anything.
You should pay no attention to this matter, because it will lead to intrusive thoughts (waswasah). The madhiy or urine that may remain on the tip of the penis is a very small amount, and it is unlikely that the water would be changed by it.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: As for water, it is pure in and of itself, but if it is mixed with some impurity and that impurity becomes apparent in it, using it means using that impure thing; it is only prohibited to use it because it is mixed with something impure, not because it is impure in and of itself. If there is no sign of it being mixed with something impure, then to think that it is impure when the water is still good and there is no sign of change in it is causing too much hardship for oneself, which is something that Allah wanted our religion to be free of; it also comes under the heading of the burdens and shackles from which Islam has relieved us.
It is soundly narrated that `Umar ibn al-Khattab (may Allah be pleased with him) did wudu’ from a vessel belonging to some Christians, when there was the possibility that it may not have been pure. `Umar ibn al-Khattab (may Allah be pleased with him) and a companion of his passed under a downspout, and his companion said: O owner of the downspout, is your water pure or impure? `Umar said: O owner of the downspout, do not tell him, for this man is confused.
Leading scholars such as Ahmad and others commented on this issue and stated that if water falls on a person from a downspout or the like and there is nothing to indicate that it is impure, then he does not have to ask about it; rather it is disliked (makruh) for him to do that.
End quote from al-Fatawa al-Kubra, 1/225, 226.
Our advice is to sprinkle some water over the place where the impurity is, and to wash it, and that is sufficient. If any of that water gets onto your body, do not pay any attention to it, unless you are certain that the water was changed by the impurity. In that case, you should wash the place that the water got onto, but in most cases the water will not be changed by this small amount of impurity. You should beware of intrusive thoughts (waswasah), for that is a disease and is something bad.
And Allah knows best.