Jonas German Keuschheitsgürtel does specify gürtel, belt, within it, but not sure about usage
Most likely, in all European languages, the "chastity belt" will contain the word "belt", because it is a linguistic calque from medieval Latin, in which theological treatises were written. They contain the term "cingulum castitatis" (literally a chastity belt) which is a theological metaphor for the fight against carnal desire. This concept is much older than the device currently referred to by the same name.
In German, the term "Keuschheitsgürtel für männer" (chastity belt for men) certainly includes cages as well. I don't know if there is a word for "chastity device".