Nikon F hands down.
The most silent Nikon is the one with the broken shutter!
or the one that was
shot and drowned
in long island sound
My black FM3A serial 28xxxxx is quiet. The mirror seems to be dampened a lot compared to my other FM3A serial 22xxxxx and FE2. At first I even thought the shutter was broken.
I had a Nikon F4 here for a few days. In fact, the sound is much less annoying than I had expected...
But I must admit, an F4 is not for me: too many buttons, even if I do not attach the MF-23 back. Is that a camera or a piano keyboard? ;) It's in my list of trades now.
To me the most silent Nikon was the F2 Photomic I had burgled from my house when I was at work about twenty five years ago, I've never heard a peep from it since :( .