1994 Honda Accord Steering wheel shakes at high speeds

Age should not be an issue. Here is a list of thing to look at.

Tire condition
How are they wearing?
Is there a bad cord in the tire?

Balance of tire
Sometimes you lose a tire weight causing the tire to be out of balance. That is a possibility.

Sometimes if you drive gravel roads or have been in a very dirty wet place there can be a build up of dirt, mud on the inside of the wheel rim. While driving the dirt is usually dispersed uniformly around the rim but if not dry when you stop it can collect at the bottom of the rim and dry. This will throw the wheel out of balance too.

You could be in need of an alignment

You could have a more serious issue with other suspension parts.