No rinse after stabilizer or final rinse! It's there to 1) stabilize the dyes and/or 2) prevent biological growth. Older stabilizer includes formaldehyde that has both effects mentioned, and newer final rinse, to be used with modern films (after about 2004-2005), has a less toxic substances to prevent biological growth, as the dyes don't need formalin anymore. But in any case, stabilizer or final rinse is the last solution, don't rinse after it.
It shouldn't leave any drying marks as it is designed to be the final solution to come contact with film. If you have problems, use distilled/demineralized water when mixing stabilizer/final rinse. And, I can't see how any spraying could help .