Are you telling us that your TV doesn't have a "baseband" video
input and you use a modulator to connect the DVD? Or that your
TV has exactly one video input and you need to switch between the
converter and the DVD?
I've never seen a converter box but I'm willing to bet it has a
"channel 3" RF output to be compatible with ALL old TVs.
If you are using RF to connect the DVD then you don't mind much
reduced quality. Tune it to a different channel and use your TV
remote to switch. But I have not seen a TV with no video inputs
made in the last 20 years.