Many timers allow you to plug your safelight in and will switch the safelight off when it switches the enlarger light on and vice-versa. An external adaptor to use the timer's enlarger lamp output to switch between the enlarger and a safelight could be made but you are dealing with mains voltages, at least on the safelight side, and would need to know what you are doing (though the circuit could be simply a relay, depending on the enlarger lamp voltage and whether it is DC or AC). Simpler to just put an inline switch used for table lamps from a DIY store in the safelight power lead and do it manually.
You are correct about the Duka: according to the instructions, it takes several minutes to reach it's correct working colour after switching on.
Cheers, Bob.