Answered by Shaykh Faraz Rabbani
If one believes that the present prayer be missed one performs mandatory ghusl, can he simply perform a quick wudu and waive the mandatory performance of ghusl until after he has prayed?
No, one couldn’t limit oneself to wudu or even dry ablutions (tayammum) in such a case. [al-Hadiyya al-`Ala’iyya]
It would remain obligatory to perform ghusl and pray, even if outside the time. After prayer, one should seek forgiveness for one’s error, or for that which led to it.