Looks like a restart is required after setting the ports for the SNMP connection handler.

$ dsconfig set-connection-handler-prop --port 4444 --hostname desktop.example.com --bindDN "cn=Directory Manager" --bindPassword password --handler-name "SNMP Connection Handler" --set enabled:true --set opendmk-jarfile:/path/to/jdmk/lib/jdmkrt.jar --trustAll --no-prompt
$ dsconfig set-connection-handler-prop --port 4444 --hostname desktop.example.com --bindDN "cn=Directory Manager" --bindPassword password --handler-name "SNMP Connection Handler" --set listen-port:11161 --set trap-port:11162 --trustAll --no-prompt
$ snmpwalk -v 2c -c OpenDJ@OpenDJ localhost:11161 mib-2.66.1.1.2.1
Timeout: No Response from localhost:11161
$ lsof -i:11161
$ ./stop-ds --restart
...
$ lsof -i:11161COMMAND  PID USER   FD   TYPE             DEVICE SIZE/OFF NODE NAME
java    1987 mark   78u  IPv6 0xffffff800b8ac0a0      0t0  UDP *:suncacao-snmp
$ snmpwalk -v 2c -c OpenDJ@OpenDJ localhost:11161 mib-2.66.1.1.2.1
SNMPv2-SMI::mib-2.66.1.1.2.1 = STRING: "/path/to/OpenDJ-2.5.0-20120616"