ALL DS games work on a 3DS. I can't trade on HG/SS myself, however, as a connection either has to be a WEP connection or an unsecured connection (the AEP2 connection here won't work even on a 3DS even though I can trade on B/W/B2/W2, as you've clearly witnessed :) ).
So if you have an unsecure connection, any Internet-connecting game WILL work for going online. However, some still will not work on some connections. This is because the games were not designed with the 3DS in mind for online connectivity. I have a puzzle game that lets you connect, but I have not been able to do so.