I hear tsaharaim every day left and right. I have never heard a common Hebrew speaker utter tsahoraim.There is no form as "tsaharaim".
You may say: tsahoraim (as the Saphardi)
tsohoraim (as modern (if we ignore all of the other accents))
The leter H is with Hataph-Qamats and must be with an o sound.
We will leave the "wise" of Egypt for now.The Tiberian Qamats was not in use except by the Tiberian people and the "wise" of Egypt.
What is this "tsuhr"?so as for צהרים (its singular: צהר)
it is based on the form "tsuhr"
the original vowel is "u" - therefore, Modern Hebrew insists on the "o" sound and pronounces it "tsohoraim".
the form of "tsuhr+aim"...
Isaac Fried, Boston University