The simplest approach is usually the best thing: print a lid for your mug and your problem is solved. Make it from ABS to hold it longer … Enjoy the tea.
But keep in mind that vibration isolators keep vibrational energy on the side of the exitation => It"ll be helpful for a desk bump but you’ll need to be more careful when putting down a full cup.
I suggest you print my Dyson drinks holder and keep your drink upright whilst doing a household chore.
It uses the mystical art of gyroscopic rings to keep the drink safe at most angles, even whilse hiding the evidence you walked in mud rather than taking your shoes off at the door as your wife keeps telling you to do.