1. Your point is correct according to the explanation of Rashi and Tosfos here and elsewhere, since they explain that we expound the letter "Heh" as a letter "Ches" only because of the "unusual" spelling ("Masores") of the word "Hinaki" -- it is written without a "Yud." According to this, making the "Heh" into the letter "Ches" solves the problem by removing the Chirik, and if so it apparently is read "Chanaki," as you wrote.

2. However, it is important to note that when Tosfos in Sotah (17a) quotes the way explains this Derashah in Sotah, he says explicitly that we read the word as "Ch i naki" (i.e. he places a "Yud" between the "Ches" and the "Nun," which clearly implies that the "Ches" is pronounced with a Chirik).

According to this version, it would seem that we expound the letter "Heh" as a "Ches" even with no allusion from the Masores to do so. There are plenty of examples of such "freehand" interpolations of "Heh" and "Ches" (see Rashi Mo'ed Katan 2a DH Nishalhi -- Derashos of this nature abound; see, for example, Berachos 30b and 36a, and Torah Temimah (here) who discusses this at length).

(Even though Tosfos there is quoting from Rashi in Sotah, and Rashi there adds explicitly that the Derashah is based on the fact that the word "is written without a Yud," it seems clear that these words are a later addition, based on what Rashi here and elsewhere writes. Tosfos, too, does not copy these words when he quotes the words of Rashi.)

Rashi in Sotah adds that according to the reading of "Chinaki," we must split the verse and read it, "And if you did not sin [then you will not die], [but if you experienced] Tum'ah while married to your husband, then you will be killed (Chinaki)." Tosfos there points out that Rashi elsewhere in Shas (such as in our Sugya and in Shevuos) explains differently. Here he explains that the word "Chinaki" is to be read with the verse that follows it ("If you have become a Sotah...") and not with the verse in which it appears. The explanation of Rashi in Sotah certainly would seem to be forced; it does not fit well into the words of the verse at all. Why didn't he explain like he did here?

It seems that Rashi's explanation there is consistent with his approach, in that Sugya, that even though there is no hint to do so in the Masores, we nevertheless expound the letter "Heh" as a "Ches." Since there is no allusion in the wording of the verse to do so, we have no right to suggest reading the "Heh" as a "Ches" if that will necessitate reading it as part of the following verse (and making it not fit into the verse in which it appears). Therefore, Rashi in Sotah found it necessary to write that "Chinaki" is indeed read as part of the verse in which it appears, and it is not to be joined to the verse that follows it.

3. It should be pointed out that a number of Rishonim explain that even according to the Derashah of the Gemara, the word is still read as "Hinaki" without making any change in its spelling. They explain that the Gemara is expounding the word "Naki" to mean "free of" or "without," implying that her body will lose her Neshamah if she is guilty, becoming Naki, or free, of the Neshamah. (See ARUCH Erech Hinaki, cited by RAMBAN here.)

MESHECH CHOCHMAH finds a beautiful allusion in the word "Hinaki" to imply that it should be expounded in a way that is not consistent with the plain meaning of the verse. He explains that conjugation "Hinaki" implies something is to be done to her that will make her Naki. If the word only meant that she will be Patur, nothing would have to be done to her; if she is not found guilty, she is automatically Patur! Rather, the use of the word "Hinaki" implies an action that is being done to her. That act must be the strangulation, and the departure of her Neshamah from her body, in the event that she is found guilty.

M. Kornfeld