Hi Lafrog
Why isn't it practical to sing for an hour before the exam? You don't have to do that at the exam premises - do the bulk of it at home first.
Both the exams I've done so far have been preceded by a full hour's lesson (mainly spent singing
anything but my exam pieces), followed by the drive to the exam room and a quick sing-through in the warm-up room there just to ensure that everything's working properly (including the accompanist

)
This has worked for me, the lesson has left me relaxed and with my throat all properly warmed up and ready, which is one less thing to worry about on the day.
Cheers
Katyjay