No the two sided tape will not work. You are going to have to drill some holes, but there are a few things you can do. The screws that come in the kit, are not stainless steel. You need to go to the local hardware store and pick up some SS screws that closely match the ones in the kit. Trust me, they rust and look like crap, then the rust stains the fender trim. Now after you have a-lined the trim pieces, drill your holes. Then apply a small amount of clear ATV sealant to the screw, this will help seal the opening, and help with the rust.
I know you are afraid of drilling because of the fear of the fender rusting, truth is that is a valid worry. But the ss screws and ATV will help. What they will not help with is the junk at get trapped behind the trim piece, depending on where you live, this can get very harmful. Also the trim has a black rubber that covers the edge next to the body. After a year or two that rubber is gone, it will crack and tear, so be ready for it. Now the biggest complaint I have, the damn trim rubs against the paint and will rub thru it. So don't be surprised if you take them off after a year or two, and find your pretty pain messed up. Good Luck.