Greetings Statalisters

I'm conducting a research with panel data (6 years) about the impact of corporate governance on financial performance. I used graphics-box plot- and -extremes- to detect outliers. Is this the right way to go?
If it is, I found that 5 of my independent variables have very extreme outliers (I check for any data errors but none). I read a lot about how to deal with those values but I'm still lost!!!. I don't want to delete those observations because my data is small (228 observations) and we can say that those extreme values are the characterics of the individuals of the population being studied. I thought about winsorizing but I didn't find any theoretical foundation.
I would really appreciate any help and I'm sorry if my question is trivial.
Many thanks in advance.
I'm using Stata 15.1.