The "Ghost Adventures" star tells TMZ ... earlier this year he bought the infamous pair of Maui Jim sunglasses recovered from Paul's crash site, but he doesn't feel comfortable displaying them at his Haunted Museum in Las Vegas.

Instead, Zak tells us he'd like to return the shades, worn by Paul at the time of the crash, to the Walker family for free ... and he's planning to reach out to the family directly.

You'll recall ... Paul died in a fiery car crash back in November 2013 and there was a ton of outrage when the sunglasses went up for auction in 2014 for $15,000. A man who was at the crash site allegedly found them in the bushes once the wreckage was cleared.

The man who found the glasses says shortly after the crash he tried getting in touch with Paul's family but never heard back. He then put the sunglasses up for auction, but after lots of backlash ... they never sold. The owner of the auction reached out to Zak earlier this year and Zak bought them from him.

If for some reason the Walkers don't want the sunglasses, Zak says he would seek the family's permission to display them in a new memorial exhibit at his museum.

Zak's already displaying different artifacts connected to dead celebs ... including a piece of the James Dean death car, Sharon Tate's wedding dress and a Patrick Swayze tooth ... but he says he would create a special display just for Paul, if it gets to that point.