All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The majority of scholars are of the view that it is desirable to press and squeeze the penis after urinating, as this is as much as one can do in order to achieve cleanliness. Their evidence is the narration in which the Prophet said: "If anyone of you urinates, he has to press his penis three times [so that he will get all the urine out]." This narration is classified as weak. Imaam An-Nawawi said that the scholars agreed that this is a weak narration. However, Shaykh Al-Islam Ibn Taymiyyah is of the view that pressing and squeezing the penis after urinating is an innovation and leads to whispers.
Nonetheless, the closest opinion to the truth is the one of Imaam An-Nawawi as he said: 'This differs according to people, the point is that one should make sure that nothing remains in the penis which one fears will come out. Some people press their penis slightly to get rid of any urine that might remain, and some people need to repeat this more than once, and some other people do not need to do this at all. In any case, this matter should not lead a person to have whispers.'
Finally, it should be noted that what comes out of the penis is considered as impure whether he pressed his sexual organ or not, and not as the questioner mentioned that whatever comes out after pressing the organ takes the ruling of being pure, rather that is considered impure.
Allaah knows best.