Answer
(Fatwa: 502/612=B)
If you do not find a time in which you can offer salah with taharah (free from breaking wuzu) then you will be considered ma’zoor (excused) as per the Shariah. You will have to make fresh wuzu for every salah when the time of the salah is due. You can pray nawafil and recite the Quran as much as you like. But, in this condition you are not allowed to lead the prayer.
For details, please see the detailed ruling about ‘ma’zoor’ in Bahishti Zewar and act accordingly.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband