It is good to keep watermelon fresh cut for a longer shelf time, but for some materials, such as nanoparticles, are experimentally proven toxic to the plants; it might very likely pose heath hazard to humans or animals who consume them.
Is your question asking for peoples individual opinion regarding the practice of utilizing preservatives to maintain freshness in watermelon or are you asking if the application of preservatives can be utilized for fresh cut watermelon?
As with the original responder I would be seriously hesitant to suggest the treatment of food products with nanomaterials. The safety of such compounds is highly suspect at this time and would need to be subject to a significant amount of research prior to judging the safety of an individual nanomaterial. Plant essences, extracts, or essential oils have a long history of use as food preservatives. The use of one over another would depend on the users preferences and desires. Also while many seemingly benign compounds can be isolated from plants it is also possible that in concentrated form this same chemicals could have deleterious effect on human health. Fruit acids e.g. citric acid, ascorbic acid are widely employed as preservatives due to an effect on both pH and oxidation reactions. They will in many cases alter the taste of the preserved product. An interesting possibility might be the use of Piper nigrum (many people enjoy the subtle flavor enhancement offered by black pepper on watermelon) as it has a very long history of use as a food preservative likely due to phenolic compounds such as piperine.
It might help to speak with food scientists for the most appropriate methods of preservation. They tend to be more knowledgeable in the field of food preservation then individuals in the plant sciences. I do not have extensive experience in the preservation of fruits I would tend to think that citric, ascorbic, or one of the similar acids would be of use. They have a long history of use in food preservation and are Generally Recognized As Safe (GRAS). An issue you will face in the preservation of watermelon (cut watermelon especially) is the high water content and sugar content. This tends to foster the growth of food spoiling organisms. The acids I mentioned can lower the pH, which will inhibit some organisms from growing. The exact quantities of any preservative required for adequate food preservation is somewhat case specific. As I mentioned earlier, this is the sort of information that a food scientist might be able to provide you with.