I would put a register button on the event/ page via the node.tpl.php file. If all your nodes are not registerable, then you can check the node by getting the $nid with $node->nid and run a db_query on the url_alias table to see if current node qualifies.
<?php
$nid = $node->nid;
$result = db_query('SELECT alias FROM {url_alias} WHERE source = :source,
array(':source' => 'node/'.$nid));
foreach ($result as $r) {
$alias = $r->alias;
}
if (strpos($alias, 'events')) {
?> <input... or <button...
Have your register button redirect to events/register/$node->title page and make sure you pass the node. There's a few different ways to go from here. If you have questions about this part open another thread.