That's a problem of aim, not spray formation, and thus beyond my expertise. The Rayleigh regimes produce large droplets (mainly diameters similar to the orifice) and not a finer spray that could go everywhere.

Also: Peeing into only the bowl won't necessarily minimize the mess. Air gets "entrained" into the water and that creates splatter. Best practice is to target the porcelain inside the bowl (just above the water line) and adjust the distance so that the stream has broken up less as droplets will create more splatter than a solid stream.