There are timers available that can deal with the power required to drive a cold cathode enlarger. I have used cold cathode enlargers for most of the 28 years I've made prints and in my opinion the biggest problem you have to overcome is the variation in the illumination as the enlarger warms up and cools down, in addition to voltage fluctuation in the power supply to your darkroom. My early experiences with cold cathode were that after making a test strip the print made could be much lighter because the enlarger had not reached the working temperature. I overcame the problem by leaving the lamp on and covering up the head while I was not exposing the paper. It was a pain but it worked.
The problem was solved when I purchased a Zone VI enalarger with a compensating timer. This works by placing a probe in the lamp houseing that reads the intensity of the illumination and adjusts the speed of the timer accordingly. In effect when the light is brighter the timer speeds up and when it is dimmer it slows down, and it works. I started with a Zone VI compensating timer and replaced it with RH Designs Stop Clock Pro timer which is also an f stop timer. I would suggest that you have a look at their web site and perhaps email them for advice, they are very helpful. The web address is rhdesigns.com