While it would seem at first glance that he is dominantly right-handed he does not seem to do everything that normally would be done be a 'right-hander.'
For instance I say that he is predominantly right-handed because of instances like this (image below), where he is using his right hand to control his pipe--which he is using almost as a finger or pointing stick to make a point. This would be much more likely to occur with someone who is right-handed.
Also, he shakes hands with Dawson with his right hand (image below.) While this could be because Dawson is right-handed and Basil is matching him, again it is more likely if he is right handed.