Bypass the Silvertone's two-pole on-off switch on the A and B supply. Then use on-off switch for the A and B supply transformer primaries.
Unless this is set requires an external antenna (and earth grounding of the chassis) , grounding the chassis even using the neutral may not be a good idea since it was not designed for "hot" operation.
The step-down/step-up transformer pair for your B supply as Tom says can be had from common wall-warts. I used a trans having a 70-volt secondary (from a defunct Jerrold channel strip amp) and some resistors/caps for 90, 45 and 22.5 volt "B" supplies as required by the AK. I agree actively filtering with a zener and power tab is better.
The "A" supply for filaments is best done using a standard filament transformer like RCA2000 suggests. I need to try this myself. v
Another method for "hum control" on A supply to filaments is to use a 20 ohm wirewound pot to balance (thus cancel) hum by varying the ground reference like on this set
http://www.nostalgiaair.org/PagesByM...7/M0044007.pdf