Goody! An easy one!
Phone around to the fabric shops in your area. They sell self adhesive Velcro hook and loop straping by the foot, yard or meter. The straps are self adhesive; you just peel off the backing paper and stick the Velcro on. It comes in white and black and in various widths. I was told that people use it for making clothes for pregnant women so that the clothes can be made to fit even though the body shape changes.
I just tried a piece of white 1 inch wide self adhesive Velcro hook strip on some polyethylene vapour barrier, and it has good initial tack, and also pulls off cleanly. I think that if it sticks to polyethylene vapour barrier, it would probably stick to HDPE.
However, if you end up having trouble getting the Velcro to stick well to the HDPE, keep in mind that the DuPont housewrap called "Tyvek" is made out of HDPE fibers. You should be able to use that red 2 inch wide Tyvek tape to stick well to the HDPE plastic, and then stick the Velcro to the red tape.
I've been told that people use Tyvek fabric to make tents, and they join the seams with double sided carpet tape because it both sticks well to Tyvek and is also flexible and waterproof. You could simply stick the HDPE plastic to your cart with double sided carpet tape.