The simplest solution is to use String.concat:
let final_string = String.concat ", " (SS.elements set_obj)
To skip the intermediate list, you could use
let final_string =
let buf = Buffer.create 128 in
let sep = ref "" in
SS.iter (fun s -> Buffer.add_string buf !sep; sep := ", "; Buffer.add_string s) set_obj;
Buffer.contents set_obj