I suggest that you should not wire it through the ignition switch. You can connect the radio power lead to either the load side of the ammeter or the hot side of the ignition switch, whichever is more convenient. I expect that the hot side of the ignition switch is easier to access.
The concern is that the contact points in the ignition switch cannot handle very much current. It is easy to overload them. Over the years there have been numerous posts about adding a switched relay to power accessories on these older Chevy’s.
On my ‘37 the only items that are powered through the ignition switch are the ignition, the fuel gauge, and the turn signals. I can get away with that because the turns signals are a short term and intermittent load. The blower motors for the heater and defroster are wired to the hot side if the ignition switch. I have to remember to turn them off when I stop the engine. I expect those motors would be too much load for the ignition switch contacts. I have never installed the original ‘37 radio I have.
