Is the absence of the sensation of ejaculation and the amount of fluid sufficient to determine that what is discharged is madhy (pre-ejaculatory fluid), and is it permissible to forgo ghusl (ritual bath) and merely sprinkle water on what affects the body and clothes when in doubt about this?

Ghusl (definition) (ritual bath) is only obligatory when one is certain that the discharge is semen (maniyy). If there is doubt, the person has a choice and can assign to it whatever ruling they wish, which is the view of the Shafi'i school. Therefore, there is no harm in simply purifying the garment and performing Wudu (ablution) when in doubt whether the discharge is semen or prostatic fluid (madhiy), especially in cases of intrusive thoughts (waswasah). It is necessary to strive against these intrusive thoughts and disregard them.