Generally you can't play video through a dvd player, though I think you can if it's also a dvd recorder.
Most players have a facility to play the stereo sound of an external device through the player's amp, but you have to connect the video cable to the television.
If you have a dvd recorder, this can receive a video picture, so you may need to look at the back and see what connections it takes. However, simple external drives usually only have a usb connection and it's unlikely the dvd has a usb facility.
There are media players available that you can stream video through or sync video to and these will have cables that will connect through a scart or other such connection. However, I think they usually require a HDMI connection or a component video connection (different to the standard tri-colour video and audio connection), so again depending on the age of the dvd recorder it may or may not be an option.
So it really depends on lots of things all working out for you. If it's a dvd player, I'd say you can't, if it's a recorder you might, but only if it's a fairly new one.