Although he has solicitors for work I don't really know who it is or which to engage for personal affairs. My sister is reluctant to make dad feel worse about his predicament by forcing the issue of wills etc onto him now whereas I would rather get this sorted whilst I still have a chance.
Is there a third person who can break the ice? Family friend, uncle, solicitor, work partner?
Someone to tell him "look, you need to make a contingency plan here asap. Don't want to leave your kids with a mess to sort out."
I'm sure your father already understands that he needs to act. Probably he is worrying about raising the issue with you.