Finally got around to implementing this. I guess I was hoping that Authorize.Net would keep postponing this change.
Anyways, thanks to @kentmorrison for his detailed instructions.
I did run into a problem, however. Instead of being forwarded to the Authorize.Net payment page, only a blank page would be displayed. I traced it down to the authorize_end.php file. My site didn't like the this line:
hikaInput::get()->set('noform',1);
So, I changed it back to the original line and the payment page would now come up:
JRequest::setVar('noform',1);
There was also a problem being forwarded back to the site. This line in authorize.php:
$value = hikaInput::get()->getString($key);
needed to be changed back to the original line:
$value = JRequest::getString($key);
Maybe that issue was because I am running an older version of HikaShop? It is rather time to get the whole cart system up to date. That's one of my summer projects.