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Secret and Secrett are English surnames, Secret and Segret are French. Dauzat ("Noms de Famille ...") explains the French names as meaning "discreet", Basil Cottle ("The Penguin Dictionary of Surnames") gives the same explanation for the English Secret. Cottle may be basing his conclusion on Dauzat; our English word does have a French origin, the surname too possibly.
However, I don't think your idea can be ignored. Unfortunately there seems to be no history of this rare surname, tracking it back to earlier forms, which would be necessary in order to answer the question you've posed.
There are English surnames, Sired, Syrett, et al., which comes from the Old English given name Sigraed ("victory-counsel"), or from the Old Norse Sigridr ( same meaning). I think it's noteworthy that in all these names the G sound is suppressed.