All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
We shall answer your question in the following points:
1- According to the preponderant view of the scholars, Maniyy is ritually pure. A group of scholars held that it is ritually impure. There is no doubt that it is better and more prudent to wash off Maniyy in order to avoid the scholarly difference of opinion.
2- As for Mathi, it is impure and must be washed off, and the stained part of the body must be purified, along with washing the penis, and some scholars said that the testicles must be washed as well. The best way to wash impurity from the body, including Mathi or Maniyy (according to the view that it is impure) is to wipe it off with a tissue or the like first and then use water. The Maaliki scholar Khaleel wrote, "It is recommended to use both water and stones in purification, in this case, using the stone first and then water..." [Mukhtasar Khaleel]
An-Nawawi wrote, "It is better to use both; stones first and then water. Using stones first reduces contact with impurity and reduces the use of water. Then water is used to purify the place completely." [Al-Majmoo‘]
3- If water is used to remove the impurity but its stickiness remains, it is not adequate to wipe it with tissues. Rather, it must be washed with water until the stickiness is removed because it is part of the impurity. The defiled area must become rough as it was (before being stained with stickiness). Kashshaaf Al-Qinaa‘ reads, "Proper purification with water means to restore the roughness of the defiled area to its condition before being tainted with the impurity and its stickiness and traces."
4- It is enough to wash the defiled area until the person believes that the impurity is most likely washed off and removed, and it is not necessary that he should know that with certainty. The Hanbali book Ar-Rawdh with its Haashiyah reads, "It is enough to believe that the impurity is most likely removed, as has been underlined by some scholars, because requesting certainty in this context constitutes difficulty and the Sharia urges the elimination of difficulty."
Allah knows best.