Ma'zoor performing umrah

Place a tissue etc. around your private area to absorb the drops. If you qualify as a ma`zoor then you will only have to make wudhu at the beginning of each namaaz time irrespective of how many times urine drops come out and you will be able to perform your umrah in that state. A ma`zoor is that person who experiences a breaker of wudhu, like passing of gas or urine incontinence etc. so frequently that from the beginning of the namaaz time until the end of the namaaz time he / she is unable to perform wudhu and read namaaz without that particular breaker of wudhu occurring. Once this is established, one will remain a ma`zoor for as long as that particular breaker of wudhu occurs at least once in the rest of the namaaz times that follow.

And Allah Ta'ala (الله تعالى) knows best.