If there as a “underline/strikethrough version of the font”, the font chooser would already show it I guess? Those aren’t font variants as far as I know. Otherwise I have no idea how you would do that.
Selecting tweaks like overline/underline/strikethrough/font color is not a feature that GtkFontChooserDialog currently has. And it is not extensible, so my advice would be to live with the limitation of the font chooser and add a separate UI for selecting tweaks like strikethrough. Or you get to do your own font chooser.