If completely replacing the old heatsink, you would need to use a Thermal Adhesive pad, not compound/grease, which the package includes.
Are you certain you couldn't just nylon wire-tie a simple 2 or 3-pin fan to the existing heatsink? I've found that works quite well for heatsinks that aren't designed with fans. If the old one has fallen off, then yeah, you'll need something like this to replace it (or a new thermal adhesive pad). However, I have seen several customer reviews on Newegg about this particular one that said the included adhesive pad does not stick well. Some also said that though the unit looks like copper, it is in fact not. It's probably anodized aluminum.