He's lovely

I brought a cat home as a child (I was always acquiring animals

)
Dad said 'it can stay the night, until we can find it a home'
Then Dad said 'it can stay the weekend, until we can find it a home'
Then Dad said 'if the dog can put up with it, it can stay.....'
We were all out one evening and came home to find the dog, the cat and Dad nose to nose on the floor in front of the fire

The cat stayed

and though tiny was always the boss

You know your cat best, but I might keep the cat in for a while when the dog arrives, just so it doesn't leave home from the stress. But let it have a safe place at home that the dog doesn't go into.