Just in case it was a typo, the Slingbox Solo does not have HDMI ports.
But if I understand you correctly but if I understand you correctly, you want to use the Slingbox as a video switch for your television.
Unfortunatelty, the output ports on the back of the Slingboxes are just pass-through connectors. So, you won't be able to redirect the composite video input to component video ouput. However, you can switch the between video inputs (composite, S-Video, and component) of the Slingbox while you watch on the Slingplayer. Just remember they all share the same audio input, so no matter which video input you select the audio will always be the same.