After urination, you should walk a little in the bathroom and having ensured the stoppage of dripping, use tissue paper and then water. If still you fear dripping, cover the part with something and walk a little, then wash it once you are completely satisfied and sure. Do not perform salah or tilawah in conditions when you feel doubtful of dripping. However, if you performed salah or tilawah, it will not be regarded invalid on the basis of doubt only.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband