Use Simple Social Icons' SVG in Scriptless Social Sharing. Note: unless you are enqueueing the SSI CSS/JS independently, these will only work on pages where an instance of the SSI widget is being output.

functions.php

<?php

add_filter( 'scriptlesssocialsharing_link_markup', 'prefix_modify_scriptless_link_markup', 10, 2 );
/**
 * Add SVG icons to Scriptless sharing buttons.
 *
 * @param $output
 *
 * @param $button
 *
 * @return string
 */
function prefix_modify_scriptless_link_markup( $output, $button ) {
	return sprintf( '<a class="button %s" target="_blank" href="%s" rel="noopener" %s>%s<span class="sss-name">%s</span></a>',
		esc_attr( $button['name'] ),
		esc_url( $button['url'] ),
		$button['data'],
		prefix_use_simple_social_icons( $button ),
		$button['label']
	);
}

/**
 * Use the SVG markup from Simple Social Icons to output in Scriptless Social Sharing.
 * @param $button
 *
 * @return string
 */
function prefix_use_simple_social_icons( $button ) {
	$markup  = '<svg role="img" class="social-' . $button['name'] . '" aria-labelledby="social-' . $button['name'] . '">';
	$markup .= '<title id="social-' . $button['name'] . '">' . $button['label'] . '</title>';
	$markup .= '<use xlink:href="' . esc_url( plugin_dir_url( __FILE__ ) . 'symbol-defs.svg#social-' . $button['name'] ) . '"></use>';
	$markup .= '</svg>';

	return sprintf( $markup );
}