The mishna forbids one to clap, bang with his hands on his thighs, or dance on Shabbat, and the gemara explains that this is out of concern that one will be metaken (lit., repair) a musical instrument.[1] The gemara[2] says that while there is a machloket regarding whether one may use a utensil to make non-musical sounds, one certainly may not use an instrument to produce pleasant sounds.
There has long been a disparity between these halachic sources and public practice. The gemara[3] says that the reason that rabbis did not protest when people clapped and danced is that it is better that people err unknowingly than knowingly. The Rama,[4] bothered by such practices in his time, comments that the concern of refusal to comply with this halacha still exists. It is also possible that people rely on Tosafot’s opinion[5] that since people do not know how to make musical instruments nowadays, the prohibition no longer applies. Although Tosafot’s thesis is surprising and not widely accepted, the Rama cites it as a second possible explanation for the lenient practice.
How far does the leniency go? The Mishna Berura[6] is among those who maintain that the Rama (reluctantly) condones only clapping, thigh-banging, and dancing, but not the use of noise-making and musical instruments. In fact, the Rama elsewhere[7] clarifies his position, writing that one may make a beat with non-instruments, whereas musical instruments may be played only by a non-Jew at a Jew’s behest. (The Rama refers to wedding celebrations, which in the past sometimes continued into Shabbat.)
Our minhag nowadays is to not use musical instruments on Shabbat (even played by non-Jews for the sake of mitzvot). The Mishna Berura[8] and contemporary poskim[9] forbid use of non-classical instruments for music, including making an audible beat while singing (e.g., “drumming” on a table); we agree. Nevertheless, it is undeniable that many serious Jews do bang on tables during zemirot. They apparently rely on the lenient opinions and the assumption that an action that augments a Shabbat-enhancing activity (e.g., davening, zemirot) is grounds for leniency, as it is a case of a mitzva. (The latter assumption is far from simple,[10] but further discussion and development are beyond our present scope). We would neither permit this nor rebuke one who “drums” in this way.
Back to your cups. Cups are not musical instruments. Is banging cups on a table worse than banging hands on a table, given that, either way, the table is a makeshift drum? Actually, using cups might be slightly worse. When hands hit various things, including each other, they produce noise. Thus, banging hands on a table may be compared to clapping, whereas beating cups on a table more closely resembles a makeshift musical instrument. Importantly, the lenient practice relates to banging hands – not instruments – on the table.[11]
You were filmed performing the song during the week, just like Jewish music artists often sing zemirot with orchestras during the week. Yet, because people might think that what you did is permitted on Shabbat (a mistake they presumably will not make regarding singing with a band), they could mistakenly imitate you on Shabbat. However, the prohibition of lifnei iver[12] does not apply to situations in which you neither facilitate nor encourage a violation. If beating with cups on a table were a clear violation of Shabbat, there would be more reason for disclaimers in order to avoid confusion. But since some rabbis would permit using the cups and most rabbis do not protest when people do something similar (i.e., banging with hands), any step you take to avoid confusion is laudable but not mandated.