Is it possible to block handhelds from dialing 411 on the BES? BES version 4.1.6.10. Or, is there a way to redirect 411 to another number? I don't believe that it can be done, but maybe I'm missing something.

Yes, you can. It's clunky to use, but it exists.
IT Policy > Firewall > Restrict Outgoing Cellular Calls

"Specify whether the BlackBerry device firewall blocks calls that the user makes unless the calls use a set fixed dialing pattern.

Type one or more fixed dialing number (FDN) patterns (for example, specific dialing numbers, or a set of dialing numbers with the same prefix) separated by a semi-colon. For example, type "+1...;1..." to permit calls from numbers preceded by 1 or +1 only.
Append "r" to a pattern to prevent calls using that specific pattern. For example, type "011...r" to prevent calls in the format 011NNNNNNNNNN. Type "r" in the pattern list to indicate that all other patterns are not permitted. For example, to allow phone calls from the number 5198881234 only, type "+15198881234;+15198881234;r".
The BlackBerry device must subscribe to caller ID to use this IT policy rule setting. This IT policy rule does not affect the emergency calling functionality on the BlackBerry device.

This rule applies only to Java-based BlackBerry devices version 4.3.0 and higher."