According to Shemirat Shabbat K'Hilchato as cited here, there is a leniency regarding oil, which is how Wikipedia describes this product:
Regarding applying hair cream on Shabbat, Shemirat Shabbat Kehilkhatah
writes that one may be lenient and apply hair oil, but only in small
quantities so that one should not come to squeeze it out of the hair.
However, he prohibits the use of hair cream in any quantity. His view
is shared by responsa Be’er Moshe. Ma’amar Mordekhai, writes that in
his day the minhag was to rub the hair on Shabbat with a mixture of
liquid fats and perfume and states: "I worry that people who do this
are guilty of breaking Shabbat, as it appears to be prohibited because
of smoothing (on the cream)." Rabbi Ovadia Yoseph prohibits this and
writes: "Since the person intends for this lotion to remain on his
hair, there is no Torah prohibition; nevertheless, it is forbidden
from the Rabbis."
Please use this info as material to show your Rav and ask him. The citations implies various opinions.
There also may be a separate concern of possible prohibition of gozez which may occur if you accidentally pull out your hair during the process of rubbing the oil in your beard. I have not addressed this issue, here. You can get more info on hair handling and gozez from this article.