Option 1 solution is actually possible through styled-component API:

import React from 'react';
import styled, {StyleSheetManager} from 'styled-components';
import NewWindow from 'react-new-window';

class Parent extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      showPopout: false,
    };
    this.nwRef = React.createRef();
  }

  render () {
    ... some stuff
    this.state.showPopout && (
    <StyleSheetManager target={this.nwRef.current}>
      <NewWindow
        title="Title"
        features={{width: '960px', height: '600px'}}
        onUnload={() => this.setState({showPopout: false})}
      >
        <div ref={this.nwRef}>
          <Popout isPopout={true}>
            ... popup stuff
          </Popout>
        </div>
      </NewWindow>
    </StyleSheetManager>
  )}
}