There seems to be a problem with version 1.94-1 of the Cygwin ca-certificates package where the files containing the trusted certificates are empty. This results in no HTTPS sites being trusted when using commands such as git, curl, and wget.
From what I can tell, the problem stems from changes that were made in version 1.94-1. In prior versions of ca-certificates, the ca-bundle.crt and ca-bundle.trust.crt files located in the /usr/ssl/certs directory were actual files containing the trusted certificates. In version 1.94-1, I've found these to be links pointing to /etc/pki/ca-trust/extracted/pem/tls-ca-bundle.pem and /etc/pki/ca-trust/extracted/openssl/ca-bundle.trust.crt respectively which are both EMPTY.
The work-around for this issue that I originally posted should no longer be necessary. Instead, upgrading to p11-kit-trust-0.18.7-2 and ca-certificates-1.96-2 should take care of it. A big thanks to Yaakov from Cygwin Ports for getting it fixed and sharing this information on my web site.