What should I do about the problem of my clothes getting wet at work: should I pray Dhuhr on time despite the impurity, or delay it until I get home, after its time has passed, to repeat Wudu?

If the wetness mentioned is from vaginal secretions, it is pure but nullifies ablution (Wudu'). Prayer must be performed at its appointed time. If the secretions are continuous, then ablution is required for each prayer after its time has begun.

If the wetness is urine: If you are afflicted with incontinence, then you must protect yourself with a cloth and perform ablution after the time for prayer has begun. It is permissible to combine two prayers according to the Hanbalis. If you are not afflicted with incontinence, then it is obligatory to purify the impurity, perform ablution, and pray at the appointed time. If removing the impurity is difficult, then it is permissible to combine two prayers according to the Hanbalis.