In React Router v4 and above, the use of `this.context` for navigation is not recommended due to changes in the way context is handled in React. Instead, React Router provides a more flexible and recommended way to programmatically navigate without mixins.

You can achieve programmatic navigation in React Router without mixins by using the `history` object provided by React Router. `history` is a library that manages session history and allows you to navigate using JavaScript.

To programmatically navigate in React Router, you can access the `history` object from the props passed down by React Router or use the `withRouter` higher-order component to inject the `history` object into your component.

Here's an example of how you can do programmatic navigation in React Router without using mixins:

```javascript
import React from 'react';
import { withRouter } from 'react-router';

class MyComponent extends React.Component {
// Function to handle navigation
handleNavigation = (path) => {
this.props.history.push(path);
}

render() {
return (

);
}
}

// Wrap your component with withRouter to access the history object
export default withRouter(MyComponent);
```

In the above example, `this.props.history.push(path)` is used to programmatically navigate to the specified path when an option is selected in the dropdown.

By using the `history` object provided by React Router, you can achieve programmatic navigation without relying on mixins in React Router v4 and above.