Third-party liability: via your towing vehicle
Damage the trailer causes to others is covered by the motor liability insurance of your towing vehicle: by law, that insurance also extends to liability for damage caused by the trailer (Art. 69 para. 2 lit. a SVG). The keeper of the towing vehicle is liable for such damage (Art. 69 para. 1 SVG).
You therefore need a registered towing vehicle with valid liability insurance. Any deductible, premium increase or loss of no-claims bonus with your insurer is at your expense.