Two levels of Controls are applied to the LINK UP/DOWN Traps.
1. At SNMP Level
2. At interface Level
At interface Level the LINK UP/DOWN Traps are enabled by default. (snmp trap link-status)
But at SNMP level no traps are enabled by default.
So even if at the interface level LINK UP Traps are enabled , unless "snmp-server enable traps snmp linkup linkdown" is configured, SNMP Agent doesn't allow the LINK UP/DOWN traps to go out.
Which means you would then have to go disable interfaces as you thought.