gavra, don’t know how you are making that kind of a distinction between partial treif and totally treif. In fact, if a store (i.e. coffee shop) sells some kosher and some non kosher, there may be a heter to got in and buy kosher. It says one who is famished, and has nowhere else to eat (in place of tzar and loss) is allowed to walk into a non-kosher restaurant and eat any kosher food which they may serve (coffee etc). So obviously without that hardship it wouldn’t apply. Also see Igros Moshe O.C. 4:82.
In any event, see what Rav Belsky said above, I cited – based on Rav Moshe.