You absolutely risk personal liability, and are certainly not paranoid to be concerned about it.

You really should consider some sort of professional liability insurance. NAFI offers a policy. Even if you can only afford the lowest liability limits, you will still receive legal defense, which is a major consideration. Even if you ultimately have no liability the legal costs of defending yourself can be enormous. And of course if you're an independent CFI the premium would be tax-deductible.

Be careful about CFI Non-owned policies, which provide coverage for aircraft damage but not professional liability.

It's really difficult in most states to disclaim or have someone waive professional liability. If you are thinking about doing this in lieu of having insurance coverage, I would consult an attorney in your state.