Radio restorers use a power supply with an adjustable current limiter (limits the current before it smokes).
Old radios sitting for a long time can have a multitude of problems.
Changing out NOS capacitors is good start but other NOS components age out as well.
If you hook it up to a 6 volt battery and turn the switch on, it can cause damage to good components so the most cautious move would be to isolate the other parts from the power supply and work in steps.
There are radio repair forums that have grumpy old guys just like Stovebolt that can help but you have to convince them that you are a novice and have a little electrical background.
If you want to do a complete restoration, you will need the test equipment to do an AM alignment.
Tuners pick up a lot of noise from dirty (dusty) bearings. It sounds scratchy when you tune it.
You need a professional grade cleaner and lube made just for electrical equipment and not spray lube from FLAPS which would be a catastrophe.

I believe I'm correct on this and I'm not sure of the year cutoff date for Delco radios.
The original speaker doesn't have a magnet to attract-repel the voice coil like a modern speaker and may have another coil that the amplifier operates.
It can be converted to a magnet speaker.

You need a bracket to hold the speaker and a bracket to hold the chassis. Message me for pictures.

"Adding CFM to a truck will only help at engine speeds you don't want to use."
"I found there was nothing to gain beyond 400 CFM."