You're better off using the S-video connection.
What you're saying you want to do is to "dumb down" a component signal into a composite input. The TV will be the limiting factor here, not the uniit or it's means of signal transfer.
First off, I'm not too sure such a device exists at a reasonable cost. Secondly, while it might allow you to "cross-connect" those two formats, the quality will still be no better than had you gone straight composite.
Again, since you indicate it's available on both units, simply use the S-video connection.