Have your tried industrial grade vinegar, soaking it and rubbing into the wood with fine steel wool?

Not yet, but just finally got my hands on double strength cleaning vinegar! Its hard to find in Canada but you can special order it from Home Hardware. Will tackle it and let you know how it goes. Thank you for the suggestion.

Try closing it with charcoal inside.

I had the same situation with a dresser. Nothing I wiped it out with worked. So I got a couple odor absorbing tubs, placed them in the empty drawers and every few days I'd rotate them to a different drawer. I left all the drawers cracked open maybe 3" - 4" because the odor absorbers work better with some air circulation. It took a few weeks but it did get the perfume smell out.

I use odor absorbers in rentals between tenants so have tried several brands. (Note: these aren't air fresheners that mask odors, they actually do absorb them.) Natural Magic is my preferred brand and what I used in my dresser. And I use the gel form, not a fan of the beads. Citrus Magic brand is also good. Avoid dollar store brands, they are a bit less expensive but don't work as well in my experience.