Got an outlet controlled by a wall switch? Plug it into that with the switch off and flip it on...Worst case scenario you trip the house breaker and have a bit of smoke(may be good to run an extension cord outside if you don't like smoke). Flip it off (the switch!
) if you notice signs of trouble.
Most tube clock radios were series string. Unless the clock motor or power wires shorted there is not much danger plugging them in, any major fault in the radio section will usually at worst burn out the power rectifier tube, another tube or some easily obtained part.
You will probably need to replace the electrolytic and paper caps for it to work correctly. (if the lytics are badly shorted that may kill the power rectifier tube.)