mysqldump
accepts ssl
arguments:
--ssl Enable SSL for connection (automatically enabled with
other flags).
--ssl-ca=name CA file in PEM format (check OpenSSL docs, implies
--ssl).
--ssl-capath=name CA directory (check OpenSSL docs, implies --ssl).
--ssl-cert=name X509 cert in PEM format (implies --ssl).
--ssl-cipher=name SSL cipher to use (implies --ssl).
--ssl-key=name X509 key in PEM format (implies --ssl).
--ssl-verify-server-cert
Verify server's "Common Name" in its cert against
hostname used when connecting. This option is disabled by
default.
Set up the proper certs and it should be straightforward. Good details are here.