How about using condition to change the readmore links.
Here is an sample code which returns a different read more text based upon the category of post. You should read the official codex page to know more about other conditional tags you can use in wordpress.
Usage - put this code into your theme's functions.php file. This code will replace the continue reading with View Image if post is in image category.
<?php
function wpse_60184_new_readmore_link( $more ) {
$read_more_link_2 = "View Image";
if ( in_category( 'image' )) {
return $read_more_link_2;
}
}
add_filter('excerpt_more', 'wpse_60184_new_readmore_link');
?>