Can I translate nodes and provide access to their translated content without the use of a site-wide language switcher?
A simple solution in such cases would be to remove the language switcher and provide for translated content only modal links:

&lt;a class="use-ajax" data-dialog-type="modal" data-dialog-options="{&amp;quot;width&amp;quot;:800}" href="/fr/node/1"&gt;French version&lt;/a&gt;


You could add the links to the node, in a template or preprocess hook. Or create a block (View or custom block plugin), which lists the available translations of the current node as modal links.

How to build such links see How to open a popup form from a view link?