He's only a Westie, therefore can't be that big. Still, if you won't have him on your lap anymore, consider having him on the floor in the footwell on your side.
It may just work and you might find that, as long as you are not too inconvenienced, i.e. that you still have enough footroom, he might curl up there and go to sleep.
Might not work or could be too impractical but it's worth a try.
Try pushing your seat back as far as possible, pop him at your feet and see what happens. Good luck.