I used to have a USB cable that split into a PSP power connector and a mini USB. I'd guess that would allow charging from a USB wall socket rather than needing a powered on USB host device, just use the PSP power connector part rather than the mini USB connector to do the charging.
Not sure where I left it now as it's been ages since I used the PSP, will have to have a bit of a dig around and see if I can find it again now.
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