Definitely use a Variac, not only because of the higher than normal voltage coming into your home, but also because of the danger of blowing the power supply electrolytic capacitors like Happy Jack said. Blown caps are very messy and have the potential to do more damage to the power transformer than your high mains voltage.
I restore old shortwave receivers and transmitters, and I would recommend that you do the following:
First, safely rig up a fuse in the AC line unless the radio is already fused, which is unlikely. A catastrophic failure that could damage the power transformer might take out the fuse before it's too late. Not a guarantee, but a reasonable precautionary measure. I never operate equipment that isn't fused. You should try 5 Amps, no more.
Second, I recommend grounding the chassis before you plug the radio in. I'm not familiar with the AK Model 42, so before grounding the chassis you should first check the schematic to ensure that neither leg of the AC line is connected to the chassis like some old radios were (since this one has a power transformer it's not likely to be the case here, but check the print first; I think that design technique came years later). The ground wire will protect you from a short in the primary of the power transformer, a shorted AC bypass capacitor if you radio has them, and a host of other evils.
Third, do a close visual inspection of the top and bottom of the chassis and look for anything out of the ordinary like burned components, tar or any other unusual discharge from the power transformer. Also look at the electrolytic cans: it was commonplace in the day to use liquid-filled caps and if your radio still has them you'll likely find that they have leaked (dried light-colored powder evident where the wires exit the bottom of the can). If you find that, don' even think about powering up the radio, Variac or no, until you replace the caps.
Also regarding the capacitors, if they are the originals or replacements of the same type as originals (liquid-filled, with wires coming out the bottom though a crimped rubber seal) again, don't power it up until you replace them. It would be miraculous if the originals are good, or even safe to apply power to.
Next, make sure that the speaker is connected; many of the old sets had a voice coil in the speaker that was also part of the power supply filter circuit.
When you apply power, bring it up slowly from zero, gradually bringing it up to around 50 VAC and let it hang there for several minutes while you use all of your senses except taste to monitor what's happening. Be alert for smoke, unusual smells, arcs, popping or sizzling sounds, etc. Use your hand (top of the chassis only and far away from exposed connections) to feel if anything is getting warm throughout the process of bringing up the voltage. Pay particular attention to the power transformer and electrolytics; there's no way they should be getting warm at this point, or at any time during the power up sequence on the Variac. If things start to heat up, unplug immediately.
If all seems OK at this point, you can slowly bring up the voltage in 25 Volt increments and repeat the above process over the course of several minutes each time until you get up to 110 VAC, and go no higher. If any any point you hear a loud hum coming from the speaker that doesn't go away by turning down the volume control you might as well stop right there are replace the power supply electrolytics before you go any further.
Best of luck. Let us know how you make out.
Jim