You need to remove the smell, not add to it by trying to cover it up.
Try removing the drawers and taking them out into the sun...that may have to wait if your weather is like mine!
Try filling the whole thing with crumpled newspaper....close it up and leave it for several days...remove the newspaper and see what it smells like.
Another option is kitty litter, unused, of course...:-)...the kind with the odor eliminating green things.
And an expensive last resort is activated charcoal. Put as much as you can in an open container and leave it for several days....but I bet airing and newspaper will work.
If nothing works, a thinned down coat of shellac on every inside surface will seal the smell into the wood.
Linda C

Thanks for the advice!

The sun airing out will have to wait. We still have 2 ft of snow on the ground and it's starting to melt into a muddy, gross mess.

What about baking soda? I wonder if I put a cup of it into each drawer if it would help...

It's a marketing myth that baking soda removes odors....it doesn't...
I wouldn't use fabreeze as that is just a coverup...
Don't know deodorocks...but it sounds like it's worth a try.
However, activated charcole is the product used by commercial places that have odor problems...it's tried and true. Often in filters for air and in self contained stove hoods.
Good luck...perfume is particularly difficult as it's made for the smell to last and last!

I've tried activated charcoal and volcanic rock odor eliminators in musty closets and old furniture. I found volcanic rock to work the best for the money because it can be re-activated in the sunshine.

The link below is to the Container Store, but there are several other sources on the web.

Good luck.

Here is a link that might be useful: Volcanic Rock Odor Eliminator

Thanks everyone! I will try the Volcanic Rock and let everyone knows how that works. If it doesn't, I'll have to figure something else out. Wish me luck!

A pro painter told me that his company used to do
insurance work, and aftter smoke damage, they would use shellac on the wall studs after tearing out the drywall inside the wall cavities to hide the smoke smell.
So, if nothing else works, ...

I use shellac to seal in musty odors, too. I had a vanity last year that smelled of perfume even after leaving it air our for several months. It was in for stripping, but I still sealed with shellac as the first coat of finish.

If you are painting, you can use either clear dewaxed shellac or BIN primer, both made by Zinsser.

sliced apples.
Seriously. I've used them in the car to remove cigarette odors. I never noticed an apple smell afterwards.
I say "remove" because when the apples were thrown out, the cigarette smell wasn't as bad.