Upload 2 versions of the icons (light and dark) to your media manger and swatch between the sources.
For example:
if ($w('#darkModeSwitch').checked) {
//....
$w('#emailIcon').src = 'https://static.wixstatic.com/shapes/43987a_d58f.svg';//light icon
} else {
//..
$w('#emailIcon').src = 'https://static.wixstatic.com/shapes/34567d_d6rt.svg';//dark icon
}
Alternatively, you can change the SVG code (the fill and strike attributes), but I think using 2 files will be easier for you.