By running all tests in Sandbox is not going to affect anything while deploying in production env.
When you deploy a changeset it runs all tests in the prod env and its got nothing to do with classes in Sandbox without test class.
you can restrict the running of all test classes while deploying by also specifying only a single or multiple test classes by choosing the Run specified tests radio button and giving comma seperated names of the test classes to run.
Only the tests that you specify are run. Provide the names of test
classes in a comma-separated list. Code coverage requirements differ
from the default coverage requirements when using this level in
production. The executed tests must cover the class or trigger in your
change sets with a minimum of 75% code coverage. This coverage is
computed for each class or trigger individually and is different from
the overall coverage percentage.
Also take a look at the answers in the link below, there could be a pointer as to why your code is failing in prodn. Can't get code coverage over 75% when deploying to production