Is one permitted to, lechatchila, place liquid paraffin candles on the Shabbos table (these candles are solid while unlit but quickly become liquid when lit). I am assuming that the table may (or may not) vibrate and move slightly while leaning on it, cutting chalah, singing zemiros, etc.
It is permitted to use such candles, even if some vibration is caused.
The reason for this is that the vibration is not caused by any direct moving of the candles, but rather caused indirectly by people brushing against the table or other similar causes. There is no prohibition on such indirect causation, the more so where there is no intention at all of causing the candles to vibrate, and even more so when the vibration might not be caused at all (which would constitute a davar she’eino miskaven, and would be permitted even for a potential Torah transgression).
In addition, there is room to question whether such insubstantial vibration is considered ‘movement’ at all with regard to muktzeh, and it is probable that it would not be included in the definition of moving muktzeh items.