auto switch circuit design

I'm working on another project. Basically an ammo can "boom box" similar to this.

Ammo Box Speakers

I am wanting to have it auto switch between battery and outlet power without a delay. I know using a power adapter similar to that of one used for a laptop might cause a slight delay as capacitors discharge. I came up with this and wondered if it might work or is possible. The amp and battery are both 12v.

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