Zhao Yuanshan was sent by Minister Liu on the second mission, to persuade the prince to confess to His Majesty. Since the prince has already agreed, it's best to quickly send out the manpower to resolve the matter sooner.
What he meant was to find the person quickly, but he actually hoped that the person wouldn't be found, so that Prince Fu could confess to His Majesty before Lih Mian completed the investigation, allowing some initiative.
If the prince's culpability is reduced, others won't be implicated.
It hasn't been easy for the secondary advisor and Minister Wang and others to manage Prince Fu's affairs for decades, and if the prince were suspected of treason by the emperor, it would likely lead to a purge of Prince Fu's faction.