You can try your local police department, they may take care of it for you. Or, depending on the type of round, a gun collector may be interested in it. If it is only 20 years old, it is probably still good, if it was kept dry.
Are the shotshells plastic or paper? If they're plastic, they're probably still good. I found a couple old boxes of paper my grandfather had, and we soaked them in water to destroy them. (They were almost certainly bad to begin with).
If they are bad then just throw them in the trash along with the rest of the garbage. Only if you know that your rubbish removal firm absolutely forbids and prohibits the disposal of bad ammo should you not do it. Most of the rubbish firms have no prohibition against the disposal of ammo, good or bad.
Think about the huge number of good rounds that get tossed into the trash at indoor and outdoor ranges and end up in the garbage truck.
With that in mind, another option is to take the shells to a gun range. Most of them do have containers for ammo that is/has not been shot.
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