The most naive, but also probably effective and readable way to do it, would be to create two canvases (just copy the one you have) and use display: auto | none in CSS to toggle between them?
Then, depending on which canvas is visible, call proper renderer.render(...) method to update the 3D view.
(You can reuse most of the code for both canvases / renderers, too, since the only difference will the the content of the scene.)
Edit: Something like this https://jsfiddle.net/oy16r2qb. Renderers and canvases are decoupled and you are free to render whichever you need at a time (or all at once.)