HDCP is relevant only to HDMI connects. There are plenty of sat and cable boxes that can output to both analog and HDMI at the same time.
If it's a HDMI handshake issue, simply turning off the monitor could solve it. Most sat and cable boxes don't even have HDCP, though most TVs do. TVs are supposed to accept non-HDCP compliant inputs too.
Your cable box may have settings relevant to outputting to analog and HDMI that could affect what you're doing.