I think you're getting tied up here on whether it is active or not based on the handle.
In reality, your device is active irrespective of the handle as the light (which is encompassed in the blade) relies on an energy source external to the body. You could classify the battery separately as an accessory but in reality you're best combining the classification.
You're also getting tied up in what single rule to apply. I think both of your quoted rules apply as your device is both an invasive device of the oral cavity and is active.
You should therefore classify this using both rule 5 and rule 10.
Under rule 5, if the device is only intended to be used in the oral cavity as far as the pharynx, then it is Class I (Class IIa if further).
Under rule 10, if the device is intended to illuminate the patient's body in the visible spectrum, then it is also Class I.
These rules aren't mutually exclusive and you can combine them, taking the highest risk classification. In this case, they are the same risk classification and so Class I applies. If the device is used further than the pharynx, then the higher risk classification of Rule 5 would apply and Class IIa would be the result.