You're absolutely right, I can tell whether a laser cut part is present though ~forever seems to be 'a couple of months'. Eventually the smell fades. I'm particularly sensitive to fire smell (we all are but I have my reasons for being a bit more paranoid than most) so this was a real problem initially for me.

To remedy you can oversize the part a bit and then sand off the burned edge, you can lacquer or paint it to stop the carbonized wood from escaping (though adherence of lacquer and paint is poor on the burned edge) and you can (lightly) sandblast the pieces.

Edit: I've added this to the article in the 'wood' section.

I got a trash can with a lid for all my small parts and a shop vac nearby to clean out the catch tray of the laser after I cut something smelly.

I also upgraded my exhaust fan to make sure nothing got into the room. I got a variable speed DC fan so that I can leave it on a low speed after cutting something smelly to help the smell go outside until it dissipates.

I had the most issues with smell when I was using cheap wood from home Depot. When I switched to real Baltic birch the smell wasn't as bad so I think the other stuff had chemicals in it.

Acrylic still smells bad but it dissipates quickly.

Using laser-grade ply is important, because often the smell is more glue than wood. Air assist makes a big difference, as does using a well-focussed laser source with good beam quality. Failing that, try a sealer coat of shellac or polyurethane.