Can you think of any names that could be a nickname for? Frederick is not really up my alley, but I'll take all suggestions.
I honestly don't think it works as a believeable nickname for any name.
Felix might work or maybe Fritz which I know is a nickname for Frederick but might work as a name for you. I know you like how masculine Fox is how about Falkner? Means Falcon trainer and if you spelled it Faulkner it could be for William Faulkner. Another idea Rex, Lex, Dex or Dax yes as a given name. More common then Fox but you would have the problem of people would assume they were all nicknames for some other name.