No-one is going to put your dog down hun.

It's a one off incident (it is isn't it?) if they call the police your dog walker will explain that the dog was on a lead and it was the dogs claw that hurt the lady, he can explain that he is new to walking the dogs but now understands just how panicked the dog gets and will not let it happen again, state that you are seeking a behaviourist, you'll be fine.

Your dog may well need to be muzzled in the future though and completely rained in when passing people, you'll be forgiven this once but maybe not if it happens again.
You should be ok for any compensation claim from the lady as antibotics and a tetanus cost her nothing, she needed no hospital stay or has no serious wounds, the police can tell the difference I'm sure from a bite and a scratch, she can't push for the dog to be destroyed in this inst.
Just be really apologetic and tell them you will make sure that it will never happen again, if the police can even be bothered to come out for it that is.............