to all you native English speakers: Would 'he sat on the rim of the chair' be a possible translation, too? (esp. while thinking of one those wooden, round bistro chairs with a slightly elevated border as in the pic below - or a bar stool...) Or does that sound strange? (photo from www.trentfurniture.co.uk)
To me, in any context, "he sat on the rim of the chair" sounds strange. I would always say "he sat on the edge of the chair" or "he sat on the edge of his chair".
Rim is strange to my ear, it's used more for containers like the rim of a cup, or the rim of a toilet seat. Edge is used for flat surfaces like a chair. I would also say "edge of the chair" sounds strange too, "edge of the seat" seems much more natural. Chair sounds more formal, like armchair/lounge chair where you relax into it, whereas seat sounds more informal, like a fold down seat at a sporting event, where one is more likely to be on the edge from excitement.
We'll sell you the whole seat, but you'll only need the edge. Sunday, Sunday, Sunday! Monster truck rally!