The Yiddish word goy comes from the Hebrew גוים, [goyim] which literally means "nations" and is also translated "Gentiles". In Scripture, this word has no negative connotations and is even used in passages prophesying the coming of Our Lord such as Hebrews 49:6
"And he said: It is a small thing that thou shouldst be my servant to raise up the tribes of Jacob, and to convert the dregs of Israel. Behold, I have given thee to be the light of the Gentiles, that thou mayst be my salvation even to the farthest part of the earth."
In the Talmud, which was written in Hebrew and Aramaic, and also later, in Yiddish, the word is used in negative or insulting contexts but can also be used in neutral or positive contexts. In isolation, the word itself does not have a negative meaning. It may give the impression of being a derogatory word because Jewish ideas about non-Jews (especially Christians) tend to be negative so the word is often used to express negative ideas.
I see no reason to think that Jews would be uncomfortable or feel "put on the spot" if they encountered non-Jews using the word "goy". In my experience, Jews like seeing non-Jews used Yiddish words and see it as a sign of Jewish influence.
For those who don't know, the Yiddish language is a germanic language that borrows many words from Hebrew (like goyim, as mentioned above) and is written in Hebrew script. It developed in Europe in the Middle Ages and was spoken by Ashkenazi Jews. There are still speakers in modern times but it is less common.