I'm sorry to hear this. YJou say you are worried about developing cancer and that you will need someone to support you. What makes you think that this man will? He's not particularly supportive right now, is he, with his coldness towards you ... so much that you went home the other night rather than be with him? What does that say to you?
He "shuts down the conversation", you say, and calls you "emotional". This sounds controlling to me and you say yourself that it's not making you happy.
I know it's scary to be on your own, but it's even worse to be trapped with the wrong person. Been there and done that, and am now on my own which is relaxing and happy.
You feel "trapped". Don't bother with an ultimatum, he's never going to change at this stage in his life. I would tell him it's not working for you and you are ok with staying dog-walking companions but that's all. This is all you seem to be getting out of the relationship anyway.