See below for the explanation as to why you could not find it, but here is the text you are looking for:
ואשר שאל על דבר נתינת ידו לרשעים או לנכרית הנה ליתן יד לפושעים אין שום איסור בזה אם אין בזה הודאה וחיזוק להנהגותיהם בשרירות לבם ולתת יד לאשה לשון הש"ס הוא ברכות ס"א א' המרצה מעות לאשה מידו לידה כדי להסתכל בה מבואר דאם אינו מכוין לשום דבר וכש"כ שאינו עושה כדי להסתכל בה כמו מעלתו שכל מעשיו לשם שמים אין איסור בזה לרצות מעות מידו לידה ודאי אם יוכל להזהר בזה מה טוב אבל אם אי אפשר לו להנצל מזה כגון אם הנכרית הקדימה והושיט לו את ידה ואין דעתו לשום הרהור ח"ו אין להחמיר בזה ודרכיה דרכי נועם ואהבת את ה' אלקיך אמרו חכמים יומא פ"ו א' שיהא שם שמים מתאהב על ידך ולא יאמרו על יראי ה' שהם משוגעים ואינם בעלי דרך ארץ
As for your question on extending a hand to the wicked, or to a non-Jewish woman – there is no prohibition of extending a hand to sinners, unless doing so would be a form of recognition and reinforcement of their whatever-they-wish behavior; as for a woman, Talmud Brachos 61a discusses "placing coins into a woman's hand in order to gaze at her" – meaning that if he doesn't intend this, and certainly when not doing this in order to gaze, as a great person like yourself does everything for the sake of Heaven – there is no prohibition... certainly, if possible to avoid it, how great, but if impossible to be saved from it, such as if the non-Jewish woman initiated and extended her hand, and he doesn't intend anything lascivious God forbid, one should not be strict about this; the ways of the Torah are pleasant ones, and Talmud Yoma interprets "Love God" as "Cause God's reputation to be loved [by others] because of your actions"; let no one say that God-fearing people are crazy and lack civilization.
(Shalom's translation)
Explanation: You are looking it up in a different version from the one the citation is from.
There are two versions of the Nishmat Chaim. The first version published in Benei Brak in 2002 contains one volume. Siman 135 Anaf 6 in this volume is indeed the one about shaking hands with women.
The second version published in Jerusalem in 2008 contains four volumes – one each for Orach Chaim, Yoreh Deiah, Even HaEzer, and Choshen Mishpat. R. Chaim Belin wrote several responsa to a certain Shabtai Baruch. One of these contains the section you are looking for, but the respona, and their component parts, are arranged differently in the two versions. Below is a table that I have compiled showing the breakdown of the three responsa to Shabtai Baruch in the original version, and the corresponding locations of each section in the new version. As you can see, there are quite a few rearrangements in the new version. Some of these rearrangements required subtle changes in order to make them understandable (e.g. adding a couple of words of opening context that was obvious in the original version because of the section immediately preceding it that does not immediately preceed it in the new version). This apparently also led to some strange numbering arrangements in the new version, as for example Yoreh Deiah Siman 141 which begins with Anaf 11 with no indication as to what ten sections it is following.
Topic |
Benei Brak 2002 |
Jerusalem 2008 |
Minyan 1 |
7:1 |
Even HaEzer 3:4 |
Minyan 2 |
7:2 |
Yoreh Deiah 141:17/18 |
Bein Hashemashot |
7:3 |
Yoreh Deiah 143:6 |
Work Agreement |
7:4 |
Yoreh Deiah 143:7 |
Praying with Chasidim/Nusach |
7:5 |
Yoreh Deiah 143:9 |
Moving to California |
7:6 |
Yoreh Deiah 141:15 |
Singing |
7:7 |
Yoreh Deiah 141:16 |
Mikvah 1 |
106:1 |
Yoreh Deiah 141:11/143:1 |
Mikvah 2 |
106:2 |
Yoreh Deiah 143:2 |
Gentile Believability |
106:3 |
Yoreh Deiah 141:12/143:2 |
Oaths |
106:4 |
Yoreh Deiah 141:13/143:4 |
Cursing Sinners |
106:5 |
Yoreh Deiah 141:14 |
Sha'atnez |
106:6 |
Even HaEzer 3:5 |
Wife and Kids |
135:1 |
Even HaEzer 3:1 |
Mesader Kiddushin |
135:2 |
Even HaEzer 3:2 |
Women's Believability |
135:3 |
Even HaEzer 3:3 |
Women's Head Covering |
135:4 |
Yoreh Deiah 143:5 |
Conversing with Women |
135:5 |
Yoreh Deiah 143:8 |
Handshaking with Women |
135:6 |
Yoreh Deiah 141:19 |
Shechitah |
N/A |
Even HaEzer 3:6 |