Can a statement be "hissed" without any sibilants?

Yes, it's perfectly acceptable to used hissed, spat, screamed, argued, yelled, screeched, roared, or any other word which describes the vocal patterns of a person in place of said.

It's commonly used in fiction and there's no rule which says every speech pattern must be followed by "Said." By using, hissed, you're telling readers that the person did in fact hiss that statement, rather than just said it.

I don't think there can be any grammatical prohibition. We can say, "He kicked a dream" for example and it's meaningless but it's still grammatical.

If you think of someone saying those words it's easy enough to imagine them being sibilant. Try whispering the phrase then whisper it again with an excess of breath. Finally voice it and keep the strong whisper sound. It's impossible to describe accurately in text but it's certainly possible to do and gives an unmistakable impression of vehemence.

To see how other authors have used this in published books you might like to follow some of the links here Google ngram:he hissed,she hissed

One of the definitions of hiss, per Merriam-Webster online:

3. to say (something) in a loud or angry whisper

There is no mention of sibilants. Since whisper is certainly not limited to sibilants, either, it stands to reason that the act of hissing can include a phrase without sibilants.

The verb hissed has several definitions. Chief among them are:

1. to make a long “s” sound like the sound that a snake makes
2. to say something in a low angry voice
3. if people in an audience hiss, they make a long “s” sound to show that they do not like a speaker or performer

_{All definitions from Macmillan, via OneLook.com.}

Now, the fact that the sentence described as being hissed:

You fool!

(a) contains no sibilants (like the sound a snake makes), and (b) is not being performed in front of an audience, constrains the definition to "to say something in a low angry voice".

There's simply no other available definition which suits the context. Therefore, the definition of hissed being employed is #2; the sentence is fine.

This question is a matter of style, not grammar. There is no "technical" answer. I personally would recommend against using "hissed" without any sibilants, but no better word jumps instantly to my mind for this case. Good luck.

Viewed narrowly, the question posits an association between hissing and sibilants. Is it possible, however, that fricatives (/f/, /th/) should be included, as well?

If so, then the /f/ of "fool" certainly qualifies to be hissed.

I don't know if this is helpful (and this is my first posting here, so be gentle with me) -- but in the novel and screenplay to "The Silence of the Lambs" Hannibal Lecter asks Clarice Starling what fellow inmate "Multiple Miggs" said to her as she passed the latter's cell on her way to interview Lecter in the asylum. Said Lecter (referring to Miggs), "He hissed at you" -- with Anthony Hopkins as Lecter delivering perfect emphasis on the word in question. And indeed that is how Miggs uttered his question, the nature of which I hesitate to quote in full due to its extreme vulgarity but suffice to say he hissed to Clarice that his olfactory powers afforded him an awareness of Clarice's ... "scent".

What constitutes a hiss is broader than you think. Compare a snake's hiss to a cat's hiss. Pretty different, right?

You may think you can't hiss 'you fool' because there's no s in it, but put enough stress on the 'f' and you get what could be considered a hissing sound. Put enough stress on the 'y' in 'you' and you get something of a hissing sound.

It all depends on how you say it, not what you say.