Hi Netinfwpus,
You can disable the global command and then configure it on the interface level of your trunk links to ensure you still receive the up/down messages. You may also review the following documentation for more information on using logging event trunk-status:
http://www.cisco.com/c/en/us/td/docs/ios/fundamentals/command/reference/cf_book/cf_l1.html#wp1138624
Patrick
Throwing packets since 2012