At the risk of throwing shade on the idea of an independent inspection, I'm going to say that even with the inspection, you're likely to find things wrong that you'll have to fix. It could be they are things the previous owner just learned to live with. They could be the reason they're selling!
It's like buying an old house. There is going to be issues.
My first plane was a 1969 J-model with 25 hours on a rebuilt engine and an expensive independent inspection. I still found a dangerous oil leak in the Hobbs and a seat rail that slipped back during my first take-off! How were these missed by the AI? I don't know. It was a fine plane once I got a bunch of stuff fixed. My second plane I did my own prebuy, but with helpful advice from members of this club where it turned into a thorough inspection via me taking photos and sending them to the club member helping me (Thanks Ron Twente!). It's been a good plane, but once again, needs a few things fixed. At least, not many surprises.
Yes, get the inspection. But even then, be ready to find the unexpected. These are old airplanes.