const Touchable = (Component, handler) => {
  const T = ({props, children}) => {
    const Instance = React.createElement(
      Component,
      {
        ...props,
        onTouchStart: (e) => handler.touchStart(e),
        /*more listeners*/
      }, children);
  }

  return T;
}

const Button = ({props, children}) => <div>…</div>;

export default Touchable(Button, {touchStart: () => {}});

<Button>Hallo</Button>

<Button onTouchStart={…}>
  <div>…</div>
</Button>

<Button>
  <div onTouchStart={…}>…</div>
</Button>