I've been using Liquid Nails and Liquid Steel for decades, indoors and out. You can mount your pegboard on 3 or 4 metal horizontal strips, then glue the metal to the metal. It will hold. Sink the bolt heads.
If the safe interior is still attractive, I would not use the pegboard. Instead, get a sheet of 3/8" hardwood plywood, cut to fit, glue on a wood strip around the edge, drill your custom hole pattern, insert wood pegs, and stain/finish it up nicely, then mount as above. You'll get more enjoyment out of it, too.
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