I have difficulty connecting to mysticism. Can anyone recommend a hassidic thinker or a work of Hassidut that would be appealing to someone who is not into mysticism?
I would strongly recommend reading (the free version of the work) "The key to Kabbalah", written by Rabbi Nissan Dovid Dubov. The work is available online at Chabad.org.
The Lubavitcher Rebbe explains in his letter (10th of Nissan, 5741) that Jewish Mysticism has to do with the two facets of the Torah, 1) the revealed part of the Torah and, 2) the hidden part of the Torah, also known as Pnimiyut HaTorah.
Mysticism, in general, has a variety of connotations, but Jewish mysticism must necessarily be defined in terms of specific topics that have to do with the Nistar of Torah—one of the two primary facets of the Torah: Nigleh and Nistar, the revealed and the hidden. Needless to say, there can be no dichotomy between the two, because it is One Torah, given by One G‑d, to the “one people on earth.”
Jewish mysticism helps to realize the said purpose of the soul by teaching it how to recognize the spirituality of matter, and that in every physical thing, even in the inanimate, there is a “soul,” which is the creative force that has created it—a being out of non-being—and continuously keeps [it] from reverting back to its former state of non-existence.
Good luck with learning Pnimiyut HaTorah, in this case Mysticism. And, as the Rebbe writes (Letter from 24th of Marcheshvan, 5720):
Incidentally, let me add that the Vilner Gaon (not only the Baal HaTanya, mind you) writes that those who do not learn Pnimius HaTorah prolong the Golus and delay the Geulo, and that without knowledge of Pnimius HaTorah it is impossible to know properly Nigle of Torah.
Also, the second source I would recommend you is reading the Kuntres Eitz HaChayim, written by the Rebbe Rashab (Rabbi Sholom Dovber Schneersohn from Lubavitch). The Kuntres can be viewed online here.
In the overview from this Kuntres, it is explained that this Kuntres included extensive quotes from Kabbalistic texts, such as quotes from the Zohar.
Kuntres Etz HaChayim, employs far more technical wording than many other Chassidic sources. There are extensive quotes from the Zohar, the Etz HaChayim, and other Kabbalistic texts, as well as passages from the Talmud and the Midrash. The Rebbe Rashab begins with an abstract Chassidic concept, proceeds to develop its practical applications, and then, on the basis of these theoretical constructs, gives direct, pointed advice to the students of the yeshivah.
You might be interested in the teachings of the Rebbe Simcha Bunim Bonhardt, the second Grand Rebbe of Peshischa. He was a Hassidic leader that was highly critical of the emphasis on mysticism, the miraculous, veneration of leaders, etc. He taught a philosophy emphasizing critical thought, individuality and authenticity in ones relationship with God. There is a pretty good English language book on him, The Quest for Authenticity, and here's the Wikipedia page. Though he was somewhat controversial in his day, his teachings are considered foundational to many different Hasidic sects extant today.
I would strongly suggest you try the sefer Nesivos Shalom. It is a great sefer, which brings different parts of the Torah from every week's parshah to life in a beautiful way. It isn't very Kabbalistic, and any Kabbalistic ideas which he brings, he explains very well. You should also look into other seforim from this Rebbe. Including on many Festivals and on the whole spectrum of Jewish thought. It isn't considered the most hassidic sefer. However, it has a very hassidic feel. It was authored by The Slonimer Rebbe.
Additionally, I would suggest you listen to the classes given by Rabbi YY Jacobson. Especially the ones in which he explains different teachings of hassidism in an extremely easy to understand practical way. His website is theyeshiva.net.
The main thing to remember is that the one thing which is greater than all of the deepest Torah, is a simple Jew with a true yearning and desire to connect to Hashem. As one of the founding ideas of hassidic thought, which is brought from our sages, "Rachmana liba bo'ei". All Hashem desires is ones heart.
Hashem should give you Hatzlacha in everything you do. And may you merit to constantly come closer to him, through your Neshama and through our Tzaddikim.
I would recommend a central and fundamental book of Hassidut: TANYA. Here is a link for translation plus explanations (Lesson in Tanya): https://www.chabad.org/library/tanya/tanya_cdo/aid/6237/jewish/Lessons-in-Tanya.htm
Since you want something appealing that is not mysticism, maybe start by learning the 3rd part of Tanya called Igeret HaTeshuva, very practical.