I believe two pieces of nylon rope such as clothesline would work. You can prevent wandering by trying a rope to each end of the handle. The distance between each end of the handle and the trunk hook should be less than two feet. I'd cut my ropes four feet long to have plenty of room for knots. (I like to wet the thumb and forefinger of a leather glove, hold the end of a synthetic rope over a flame, and roll the melted end between the thumb and forefinger of the glove to prevent unraveling.)
Clove hitches might work around the handle, but I'd use constrictor or miller's knots to make sure they didn't slide along the handle. A miller's knot is like a clove hitch, but you add an overhand knot where the two lines pass under the crossover turn.