Suppress Time Machine Old Backups Dialogue Via Command Line
I don’t know whether you can suppress the dialog through tmutil directly.

The alternative, as you suggested, is to temporarily turn off the “Notify after old backups are deleted” option of the Time Machine options preferences through defaults:

sudo defaults write /Library/Preferences/com.apple.TimeMachine.plist AlwaysShowDeletedBackupsWarning 0


Use “1” instead of “0” to turn the option back on.

(I should perhaps specify that this answer applies to El Capitan, I don’t know about Sierra, though I assume this hasn’t changed.)