al-Istinjah is not a condition with every wudhu, and indeed that which obligates istinjah is urination or defecation and that which comes by way of them. As for other than them, from the things that nullify the wudhu, such as passing wind, touching the private parts, eating the meat of the camel, sleep, the Istinjah is not legislated for them, rather the prescribed wudhu is sufficient for that, and that is:
Washing the face, and that includes rinsing the mouth and sniffing and blowing water from the nose.
Washing the hands up to the elbows.
Wiping the head along with the ears.
Washing the feet along with the ankles.
As in the saying of Allaah:
يَا أَيُّهَا الَّذِينَ آمَنُواْ إِذَا قُمْتُمْ إِلَى الصَّلاةِ فاغْسِلُواْ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى الْمَرَافِقِ وَامْسَحُواْ بِرُؤُوسِكُمْ وَأَرْجُلَكُمْ إِلَى الْكَعْبَينِ
O you who believe! When you intend to offer As-Salât (the prayer), wash your faces and your hands (forearms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to ankles. [Soorah Al-Ma'idah]