In such case you should just rewrite shopware login to your custom.
So after user sign up to shopware - you should log out him, then user got login page and he can only do login with 3 pieces, which will check on 3rd service and in case such user exist - log in to shopware. Only thing - you should bind 3rd service data with shopware data, as case - customer should use same email like on 3rd part service, or you need to add additional field for registration, where customer should fill some uniq identifier from 3rd service.
This only right way which I see for your case, in other case you can use only development mode, but it isn’t right way for perfomance reasons.