No native speaker.

Nul n’aurait pu le dire

‘aurait pu’ is the third singular of the so-called conditionnel du passé. See
https://fr.wikipedia.org/wiki/Conditionnel_pass%C3%A9_(conjugaison_fran%C3%A7aise)

The sentence, as it stands, conveys the meaning of the sentences

No one could have said it. No one could have said that. No one could have said so.

Regarding the absence of ‘pas’. Pas is not needed with the negative singular indefinite pronoun ‘nul’ (pronom indéfini singulier).

Nul n’aurait pu le dire.

Nul argument ne pourrait la convaincre ; nul n’est censé ignorer la loi

https://fr.wiktionary.org/wiki/nul#Pronom_ind%C3%A9fini

• the verbal form "aurait pu" is an instance of conditionnel passé. The (indicative) plus-que-parfait would have been "avait pu"
• "Nul" used as pronoun is a more formal form of "personne" (in the meaning of "no one"). "Nul", just like "personne", already carries the negation , so there is no need to add the adverb "pas". It would be an error.

Actually, "nul n’aurait pas pu le dire" is very awkward semantically as it is a case of double negative, which in French equates to a positive (logically, "nul n’aurait pas pu le dire" should actually mean "no one would have been unable to tell", which at best is just the opposite of what "nul n’aurait pu le dire" means). In any case, this is not a turn of phrase that a native speaker would use.

Negation is expressed in various forms in a correlative way, with more or less evidence, without losing sight of the general meaning.

The following expressions have more or less the same meaning.

Nul ne le sait. (pronom + ne)
Tous le savent.

Personne ne le sait. (pronom + ne)
Quiconque le sait.

Aucune personne ne le sait. (adj. + ne)
Chacun le sait.

Pas une personne ne le sait. (adv. + ne)
Tout le monde le sait.

Various words convey a negative meaning and form the negation when associated with ne.

Note: The negation can also be expressed with a single word (ne) in which case the negation focuses on the verb.