Since the cold cathode is still a fluorescent lamp, it contains mercury vapor and should be discarded in the same manner you would a regular CFL. The bulbs contain half the mercury of conventional "hot cathode" fluorescents and have a thinner tube diameter, which allows them to run cooler, and last up to four times as long (a lifespan of 25,000 hours). The mercury is reduced by 85% over the life of a cold cathode bulb as a regular CFL would have to be replaced three times during that period.

CFL cleanup
CFL bulbs contain a small amount of mercury - so if a bulb breaks in your home mercury vapor may continue to release from the bulb unless it is properly cleaned up.

• People and pets should leave the room. Turn off the air conditioner, furnace, and fans and open the window to air out the room for 5 to 10 minutes.
• Use stiff paper, cardboard, sticky tape, a damp paper towel or disposable wet wipes on hard surfaces to collect all the broken glass and visible powder.
• If you can, continue to air out the room where the bulb was broken for several hours. Make sure the air conditioner, furnace, and fans are off.
• Place the broken CFL and any clean up materials in a glass jar with a metal lid or a sealable plastic bag for proper disposal. 

Find more detail on cleaning up a broken CFL on the EPA website.