I don't know if the degredation is significant on the first opening of a JPEG file. However, you can also save a copy of your NEF image as a 14 or 16 bit TIFF file. TIFF's are huge files, but they do not degrade like JPEGS, and most post processing programs can read them. The only problem with the TIFF format is that it takes up a lot of storage space. I keep all of my NEFs and TIFFs on a huge external hard drive which I then back up to another huge external hard drive.
In reading your comments, I'm not sure if you are converting your NEF files JPEGs or merely saving a copy of the NEF as a JPEG. If you save your edited NEF with all of your edits, you can go back at a later date and remove or further edit the NEF. Or, you can save your edits as another NEF file and retain the original unedited NEF. I've never used View NX as an editor, but Caputre NX2 is a non-destructive editor which means that your original NEF is not permanently changed by your edits, as pointed out above.
You can download a full working trial version of Capture NX2 on the Nikon site. You may also want to check out some of the other forums and resources on this site that discuss and answer a lot of questions regarding post processing. I'm not an expert at post processing, but many of the Nikonians are, and you can pick up some good tips and information in the other forums.