No. The person a grievance is about should not investigate or hear it. You need someone independent and impartial, which can be a real challenge in a small business.
If you genuinely have no one suitable in-house, that is a common reason owners bring in an outside person to hear the grievance or run the investigation, so the process cannot later be challenged as biased.
Important
Every situation has its own details, and those details change the right answer. For a read on yours, take the free Employee Situation Check or book a call.
General guidance to help you decide your next step, not legal advice. Employment law changes, so always check the current position for your own situation.