There is a lot that go wrong when dogs are with cats unattended, even with an escape route.
As tabulahrasa said, dogs are pretty fast, often faster than a cat.
Sometimes it's the cat that is the vicious one and if the dog retaliates the result can be disastrous.
Sometimes the problem is not aggression but love.
Some cats love the dog so much that they like to follow it round, play with it, share its food etc.
I have one of these cats and a fortunately very sociable, tolerant dog.
But there have been 1 of 2 occasions where the dog has growled and shown teeth when I haven't been quick enough and the cat had tried to 'share' her food, sometimes the cat likes to jump on her head and bite her when she's sleeping - she either plays with her or (rarely) walks away but if I wasn't present whose to say she wouldnt get annoyed and discipline the cat, injuring her accidently?
Not to mention the emotional stress a cat will feel if there is a big scary dog that chases it which can lead to aggression, toileting problems or even upping sticks and moving home.
There isn't much point focussing on breeds.
most dogs will chase cats, a sizeable proportion will harm them too if they catch them.
It's across the board, there are cat chasers/killers in EVERY breed.
Generally speaking, a puppy that is taught from day one not to chase or intimidate the cats will get along fine with YOUR cats.
There is no guarantee how they will react to cats outside though.
My in laws have a jack Russell terrier and a jack Russell cross Yorkshire terrier, with two cats - high prey drive breeds
I have a working bred collie and a cat - another traditional 'no cat' breed
My BIL and SIL have a pug and a chihuahua who go mental at the sight of a cat.
I have no doubt they would attempt to kill one if they caught it - two breeds commonly thought to be low prey drive
I would probably get an older (3+) dog that is thought to be cat safe but either crate it, take it to a (good) daycare with only a few dogs or confine it to one room when your not there.