In that case, you can't have a cat petrified to come downstairs.
You NEED to force the issue and in your presence have both animals in the same room. If need be, put the dog on a leash so he can't get close to the cat.
Another method is to keep the 2 animals separated by a door, slightly ajar. So that both animals can sniff eachother (1st introduction).
Another way is to get the blankets for both animals and switch them around, so that they both get used to the smell (pre-introduction).
Basically, you have to make the judgement call yourself. There is no wrong or right. You have to make the decision yourself.
Also, do not ever trust 100% an animal to behave itself. An animal can turn. Even the softest/cutest dog can maul a cat to death (or other small animal) to death.