Since nobody else has responded, I will give it a try, First, I will assume that you are female (but I guess this could work for a male too). Rather than letting the pee flow out at its own natural speed, have you tried pushing it out faster? As an example, imagine having to pee a lot and being in a big hurry, you would use the muscles to force a harder stream of pee. This causes less dribbling all over.
Now for a totally wacky idea: Did you ever take high school chemistry? When you poured something out of a beaker, you would lean the stirring rod against the lip of the beaker so that the liquid would flow along the rod into whatever you were pouring it into rather than dripping along the side of the beaker. A drinking straw might work.