The present invention is directed to a cold seal package that includes constructions wherein two substrates, or two portions of one substrate, are sealingly engaged to one another using a substantially natural latex rubber-free contact adhesive. The two substrates can be easily peeled apart without substantial damage to the substrates. Furthermore, the substrates cannot typically be resealed, or refastened, once peeled apart. That is, the cold seal formed by the adhesive between the substrates is substantially non-refastenable. Advantageously, a cold seal package of the present invention is particularly well suited for aseptic delivery of packaged goods, such as bandages, dressings, and the like.