The area that smells is the leatherette. After some cleaning, I cannot quite detect the odor on the body of the winder (i.e. the plastic and metal). Yes, I would not attempt anything with Febreeze, as it is a rather typical chemical-oriented product.
After discussing the matter with the seller, I found out that Armor All is the culprit. He mentioned that, prior to shipping, he wipes his items with Armor All. I wish folks would stop doing this. Whether sensitive to such chemical smells (i.e. allergic) or not, no one should be inhaling chemical residues. For every chemical cover-up product, there is almost always an alternative natural product.
Thankfully, a combination treatment of baking soda and enzyme cleaner got rid of most of the odor, and I was able to keep the winder. I have fared very well in cleaning my camera equipment with these products:
Bon Ami (not Comet...Bon Ami is natural, but Comet is not)
organic enzyme cleaners
Of course, one must use care with any cleaner, but, after cleaning dozens and dozens of pieces of gear, I have yet to have any problems.
Before I forget: Meltonian leather balm works very well on the leatherette. On camera bodies and grips, I use this as my final treatment (after cleaning). If anyone has any questions, I would be happy to assist, perhaps by starting a thread on "natural camera care."