Hello,
THe button is loaded in the theme packs, in file THEME_event.php
<?php // Registration button ?>
<div class="ic-event-registration">
<?php echo $EVENT_REGISTRATION; ?>
</div>
So, by editing or creating your own theme pack for iCagenda, you can move the place in the html structure
Note that to change the styling, you can use the Custom CSS option in the global options of iCagenda, to override style without having to edit the css files, but if you create your own theme pack, you will be able to edit the css already in the component.css applied to the button, registered bubble...
Hope this helps!
Regards,
Cyril