I wouldn't worry about the miniscule amount of mercury in a CCFL that is found in a monitor.
A study on the amount of mercury from a CCFL tube study states
The New Jersey Department of Environmental Protection states in a report published in 2004 that between 17% and 40% of the mercury is vaporised if CCFLs are broken.
This is over a period of several hours, and a third of the mercury is released over the first eight hours.
In the literature, the amount of mercury in CCFLs varies between 0.1 mg/lamp and 10 mg/lamp
The study goes on to test up to 16 CCFL tubes, basically an entire large TV, smashed in a 31 litre (enclosed) box and while smashing 16 tubes does result in a potentially (long term) dangerous 0.25mg/m3 exposure level after an hour even the vaguest amount of ventilation will almost certainly result in a level well below what is considered "safe".
A single tube being smashed, i.e. the most likely outcome of an accidental drop, would give a tiny amount of vapour that even in a normal sized room probably wouldn't result in a dangerous level. Even so it could be easily combatted by simply opening the window and/or putting the broken device outside.
A brief and temporary exposure is unlikely to result in any significant harm anyway.
If you had a mercury leak then the tube would not work at all and you would have a permanent dark patch because the tube would be cracked and the atmosphere within contaminated and unable to effectively conduct the electrons that produce light. Flickering is a sign of power supply issues rather than cracked CCFL tubes leaking mercury.