Dickmann is not connotated the slightest with anything sexual in German, the language knows nothing about "dick’ as penis or such. Dickmann simply translates to “fat man”, and that also has no sexual or other connotations.

Yep, it’s that innocent over here. “Dicke Nüsse” is quite the opposite in that regard - Nüsse/nuts is a regularly used term for the testes. This part is quite raunchy.