I have a DVD player with the polarized power plug seen here.

Rather than spend $10 on a replacement cord, I have an UNpolarized cord that fits perfectly. But I don't want to damage anything.

I know on the wall outlet, the right socket is positive. Is it possible to tell which post is positive/negative based upon the DVD plug shape?

Its not really a positive in AC Volts.
AC uses a Hot and a Neutral(At Ground Potential). The ribbed half of the wire is neutral, the smooth is hot.
Electrically it will work fine, just not correct.

If you look at your receptacle, one of the two slots will be longer than the other. The longer slot is for the Neutral.

You can't really say it is always the right side because the receptacle can be installed in two different orbits.

Usually only the ground pin is tied to ground. In TV's it mattered somewhat, but usually there was always some isolation in the coax.

Polarity may matter a bit, but it could be in the form of hum. So, just reverse the plug.

The hot side is usually switched in polarized plugs. e.g The center pin is switched to ground on a lamp to lessen the possibility of a shock. The threaded side would be at ground potential. In the old days there were no polorized plugs, nor no polorized outlets. Lamps still worked.

When I was a Kid, I got shocked from a Pinball machine, unplugged it, reinserted reversed, and no more shock?
I understand now, then it just worked.