I have found many studies that used 1 mm/day to remove the drizzle effect in precipitation during bias correction. Instead of using such static value, is it okay if I can use 90% or 95 % percentile?
There is no absolute, universal threshold or method to distinguish between drizzle and precipitations. The answer to your question will depend on the reason you want to isolate those two contributions to the water balance of your system of interest.
A rational way to address this question would be
1. to clarify why you want to differentiate between drizzle and precipitation,
2. to determine what impact an erroneous threshold would have in whatever downstream application you are pursuing, and
3. to establish the maximum tolerable error you can admit before your objectives become unachievable or your results become useless.
These steps should help you determine the real importance of this distinction as well as the best way to implement it for your purposes. Remember that the "optimal" distinction between drizzle and precipitations may be different in different places and at different times (e.g., seasons), and that what works for you may not be optimal for another user or in another context.
To me, it seems like using a percentile method wouldn't really be optimal, as there's no way to really "ensure" that whatever threshold you set is actually cutting out all of the drizzle, OR that it isn't accidentally cutting out events that aren't drizzle. What "percentile" would just cover drizzle events would be different at every location. If a station receives only a trace amount of precipitation in an hour, they will just label it as whatever their minimum possible value is. Maybe that's 1mm, maybe its "T" or something else - not 100% sure. But I imagine just using the method that is most accepted in the field (1mm a day if that is in fact what is generally used) won't throw any red flags or anything.
Additionally, if you use only one or limited number of data sources, for example reanalyses, you could contact the source maintainer or seek in the source description document for some hints.