OK, I figured this one out. Pretty easy actually.
1. In wordpress admin, go to the addtoany save/share settings page.
2. UNCHECK all options for 'Placement'.
3. Click the arrow button to the right of the text that reads "* If unchecked, be sure to..." and copy the PHP code it gives you.
4. Place this in the relevant areas of your theme. For me this was in index.php and single.php pages, immediately after
<?php the_content(); ?>
5. Done! For some reason this seems to hide it from the iPhone. For me at least.
I also found some very useful mobile browser detection code, at http://papermashup.com/lightweight-mobile-browser-detection/
But in the end I didn't need it.