It is entirely appropriate. There’s nothing gendered about the expression in Modern French, though of course nothing prevents someone from making a transvestite joke after being told that.

Dans mes jupons is not gender neutral. If the expression is used by a man, it is done humorously.

There is a close but not strictly equivalent alternative that can be used for everyone:

collé aux basques

See this question for details. Edit: that question was yours too…