The word הרהור (and its plural) are the verbal noun of the verb הרהר, meaning to think, or to ponder. הרהר is in the verb form פיעל, meaning it has two syllables - a chirik under the first (root) letter, and a segol under the second to last (root) letter. (In short, הרהר is pronounced hirher).
Verbal nouns of this verb form keep the chirik sound, and replace the segol with a וּ. So הרהר=hirher, becomes הרהור=hirhur.
An example of this in tanach (since the word itself doesn't appear) is the word כפר (kiper-atoned) (see Vayikra 16:18) which becomes כיפור (kippur-atonement) (for example Vayikra 23:27).
Therefore it should be pronounced hirhurim.
['Harhur' would not be the verbal noun of any verbal form, there are too many to write here but you can find them all here, among other places: https://milimilim.co.il/%D7%A9%D7%9E%D7%95%D7%AA-%D7%94%D7%A4%D7%A2%D7%95%D7%9C%D7%94]
Another sign that it's pronounced 'hirhur' is the many places where mepharshim write the word as הירהור (which must be pronounced hirhur). For example, yerushalmi sh'vuos (1:6)
העולה מכפרת על הירהור הלב
the Olah [Korban] atones for thoughts of the heart
As well as a couple more talmudic sources, Jastrow, and many rishonim and Achronim. (The Smag, shulchan aruch, Targum yerushalmi, sfat emet, machzor vitry, another yerushalmi, and others, just from a quick search of sefaria).
After a look through the Cambridge Cairo Geniza manuscripts available online, I also managed to find one which used the spelling הירהורים:
https://cudl.lib.cam.ac.uk/view/MS-TS-NS-00121-00045/2
Another manuscript I saw spelled it הִרהוּרִים: https://www.loc.gov/resource/amedscd.2018757847/?sp=10&st=image&r=0.242,-0.161,0.731,1.099,0
(There were a few that spelled it הרהורים, but since they are not vowelized, it still makes it impossible to tell how they meant for it to be pronounced).
And even though in Daniel (4:2) it says
וְהַרְהֹרִין֙ עַֽל־מִשְׁכְּבִ֔י
This seems to be a rare case, in addition to it being in aramaic. Almost all of the other sources that I saw were either spelled with a yud or vowelized with a chirik (at least by sefaria).
At the end of the day, both pronunciations seem to have at least some sources that support them. However, the manuscripts which use the hirhurim pronunciation , as well as the general rule of פיעל verbal nouns, in addition to the list of rishonim and Achronim who spell it הירהור in other places, makes והרהורים as 'v'hirhurim' more likely.