You will need to modify the template. In this case the spHead.php template in the /templates folder of whatever SP theme you are using. You can use the SP theme editor for this.

Locate the line of code that runs this display function which will probably look like this:

sp_RegisterButton('tagClass=spControl', __sp('Register'));

You are going to add a new argument. Note the ampersand that is used as an argument separator:

sp_RegisterButton('tagClass=spControl&link=http://problem-with-post-edit-buttonpathy.com/register/', __sp('Register'));

That should do it.

As always we recommend that you create your own SP theme so that any customisation is not lost during a future update. (http://codex.simple-press.com/codex/themes/theme-basics/creating-a-theme/)