wp_generate_tag_cloud
has a filter that allows you to edit the string input. You can use regex to find and remove the inline style:
add_filter('wp_generate_tag_cloud', 'na_tag_cloud',10,1);
function na_tag_cloud($string){
return preg_replace("/style="font-size:.+pt;"https://wordpress.stackexchange.com/", '', $string);
}