I might recommend constructing some sort of barrier right at the edge of the sink counter between your fly and the sink. For example, if there is a box of tissues next to the sink, slide it in front to act as the barrier.
You could also bring something with you, say, a clipboard - you could place the clipboard up against the edge of the counter and lean up against it with your thighs and your crotch. That would definitely block all the spray - much better than some measly paper towel. Plus, it wouldn't be that weird if someone else saw you in the bathroom - you walk in with a clipboard and hold it under your arm while peeing and then when you go to wash, people will understand your hesitation to place the clipboard on the germ-infested counter top when you pin the clipboard up against the edge of the counter with your body.
