Yes, it is likely that the family crest would apply.
The original Hunzikers were from Switzerland.Prior to 1600, they constituted several families of the same name from Leerau, Leimbach, and Gontenschwil.The descendents moved down the valley during the 1500s, and by 1600 had established themselves in Reitnau, Attelwil, Staffelbach, Schoftland, Muhen, and in the stadt Aarau.In particular, a "Hunziker-Center" developed in Kirchleerau and Moosleerau with about 20 Hunziker families there after 1600.
Even at this early time, the name "Hunziker" evolved into different ways of spelling."Hunziken" was used in the Geuensee in the Luzern Suhrental."Hegi" was also used."Huntzinger" and "Hunzinger" were derivatives.My branch of the family (Hans to Melchior to 12 children...and onward), for which I have a copy of their old Swiss family tree, spelled the name "Hunsinger" of which the spelling was changed centuries later to "Unzicker".
The "basic" family crest was evident around 1600, but painted in different colors, I assume representing the many different branches of the family. It's difficult to trace the thousands of descendents of the original family for a variety of reasons: names were spelled differently over time in different countries, dates of births, deaths, and marriages were sometimes confused or associated with other descendents of the same first name, and documented links were missing.By 1759, when your Mathais Hunsinger was born, my "1600 Hans" had about 76 direct descendents throughout Europe.I did not find a "1759 Mathais" as one of them, but suspect your Mathais descended from one of the many dozens of other Swiss "Hunziker/Hunsingers" of the late 1500s/early 1600s.
You may or may not be aware that many Swiss fled their country because of religious persecution that started in the early 1500s.These were people who believed in religious freedom vs. the "State Churches" of Western Europe .In Switzerland, these people were first known as "Anabaptists".From 1527 onwards, hundreds of men and women were jailed and killed.Families fled Switzerland to areas such as the Palatinate, Alsace, Hesse, France, Luxembourg, Lorraine, Bavaria, Galicia, Volhynia, and Holland.There were two main groups: the Amish (who followed Jacob Amman) and the Mennonites (who followed Menno Simons).Unfortunately, persecution did not end in their new countries.William Penn "invited" some refugees from Switzerland to settle on his land.From 1683 onwards, many Amish came to Pennsylvania.Many Swiss Mennonites, on the other hand, remained in Europe gradually assimilating into Germany, France, and Holland. My family was in this category, but just prior to 1850 came to America.
Well, I have rambled...didn't plan to...hope I have made some elementary sense to your question of the family crest.I’m sure there are many others who know more.