Your truck is required (by law) to have tires capable of handling the maximum weight your truck is rated to carry.  This can mean either truck tires or passenger car tires.  Truck tires (LT) are much more stable and make towing more comfortable but not absolutely necessary.  I'd recommend you try it with your OEM tires and replace them with truck tires (if OEM is passenger car tires) if you feel it's necessary.  For what it's worth, those brochure numbers for tongue weight are with an empty trailer so expect it to be quite a bit more when loaded.  Best to ASSUME it will be 15% of the actual loaded trailer weight.  Conventional trailers RANGE between 10% and 15% so plan on the worst case and go with 15%
Good luck / Skip