As I said, with beginners, almost anything works. I'm not sure the attacker could hit a wine glass hard or accurately enough to break it, much less connect with or do damage to a moving human target. And so it doesn't really matter whether Graham uses a tsuba or not: his wrist isn't going to get hit hard enough for him to care.
But it is not the uke's abilities we are talking about but the teacher's. Shouldn't the teacher be technically sound regardless of how weak the uke is? Also, you don't hesitate to say that the uke is no good, why hesitate in regards to the nage?