How can I mitigate risk of electric shock?
First, never, ever ever work on a tube radio while it's plugged in!

Assuming you just want to gut out the radio circuits and keep the case, if it has been unplugged for a year, it's probably safe. 

There were two common reasons for such labels. First being, capacitors can hold lethal charges for hours to days after the circuit is powered off. The other is an abominable practice from the early 20th century of bonding the neutral wire of the power cord to the radio chassis, and counting on (1) a polarized plug, (2) correct domestic wiring, and (3) the insulating value of the case to protect the user.

If this radio is truly an antique, and you know no one has tried plugging it in recently, it should be safe enough.