Al-jawab billahi at-taufeeq (the answer with Allah’s guidance)
It is compulsory to do Istibra’ after urinating. Istibra’ is to ensure that the traces of urine has come out completely. Some examples of Istibra’: one should shake, sway or squeeze the penis very gently, coughing, taking few steps, jogging, lying on the left side etc, there is no restrictions in Istibra’, one may do Istibra’ in any way one is used to.
It will not be permissible to begin Wudhu without doing Istibra’.
(Nurul Idhah Pg.27, Hashiat Tahtawi Pg.42, Al Fiqhul Hanafi Wa Adillatuh Vol.1 Pg.38)
If however, the urine drops comes out later then you should try placing something, for example, toilet paper or cotton in your under garment so that it absorbs any left over drops of urine.
Before making Wudhu and Salah you should remove or replace it with clean toilet paper and if your private parts have been soiled with urine then you just need to wash it.
Rules regarding a Ma’zur:
A person will qualify as a Ma’zur (excused) when a person who does not find sufficient amount of time to make Wudhu and perform Salah because of any such reason i.e dripping of urine, continous passing of wind etc, which continues throughout one full Salah period, will be regarded as Ma’zur.
One will perform ablution for the time of each obligatory prayer. And, with that Wudhu it is permissible for one to pray as many obligatory or optional prayers as one desires during that prayer time. However, the Wudhu will be nullified at the expiry of the prayer time.
One must also remember, that the excuse must be continuous – for one full Salah period. If a person manages to keep his/her Wudhu for 5/10 minutes in the entire Salah period with which he/she is able to perform his/her Salah, then he/she will not be a Ma’zur. Also, If a Ma’zur (excused person) experienced another factor (laughs aloud during the prayer or vomits etc,) besides the excuse due to which he/she is classified as a Ma’zur, then his/her Wudhu will break.
(Quduri Pg.22, Nurul Idhah Pg. 51)
And Only Allah Ta’ala Knows Best.
Moulana Qamruz Zaman