Although Humrot at times can be excessive, it is prudent to avoid behaviour that would lead to unnecessary suspicion. Ramch"al in M'silat Y'sharim might term this middah as "Z'hirut"
A Merchant once taught me not to put the customer's large bill into the register right away
Rather, keep it on top;
Then make the change; and only then, after the customer is satisfied, put it into the register. This can avoid a dispute in the case EG when a customer hands you a $10.00 and claims to have given you a $20.00. By NOT depositing it right away, one is being PRO-active.
Be careful to be Zahir! ;-)