How to I force internet-bound smtp mail through the send connector instead of the routing group connector on Exchange 2010?

I just added a new Exchange 2010 server on a Server 2003 domain that has an existing Exchange 2003 server.

There is one routing group connector connecting the 2 servers.  All mail flows between the 2 servers without problems.  I have already created a new mailbox on Exchange 2010 and moved a couple of existing mailboxes from Exchange 2003 to Exchange 2010.

There is an smtp connector on the Exchange 2003 to a smart host (Appriver).

When I installed Exchange 2010, it automatically created a send connector to the same appriver smart host.

However, internet-bound outgoing mail from the Exchange 2010 server goes over the routing group connector to the Exchange 2003 server and then out to the internet (to the appriver smart host).

I would like internet-bound outgoing mail from the Exchange 2010 server to go directly to the appriver smart host, without changing the routing of the Exchange 2003 internet-bound outgoing mail.  I want each server to send it's internet-bound outgoing mail directly to the appriver smart host.

The cost of appriver send connector on the Exchange 2010 server is 1.
The cost of the routing group connector is 1.

Should I increase the cost on the routing group connector?  Will this do what I want without breaking anything?

Thanks.