Assuming the screw-on handles use the bottle stopper threading, wouldn't unscrewing the handle over time cause the threading to be too loose?
For my bottle stoppers, I had similar questions .... how to sanitize the stopper with a wood handle on it. My solution was elegant and simple. Don't glue the wood to the stopper part, just glue the metal screw into the wood and screw the stopper part on and off as needed.
There's a coarse side and a fine side to that connection screw. The coarse side matches the screw used on the bottle stopper chuck, while the fine side goes into the metal part of the stopper. By gluing the coarse side only, I leave the metal part removable, and that part is dishwasher safe.
I still advise people "hand wash only, don't use more than a damp towel on the wood". But I also tell them that if anything ever happens to the metal part, they can come back to me for a cheap (5 dollars) replacement section, and they're very happy about that option. It's the turned wood part that they want to protect.
As for your situation, it may be similar to mine, or it may not. There are still options you can use to protect your customer's investments. One is to use a trick to stabilize the wood in the threads that you cut. You simply apply superglue to the threads and spread it around with a disposable item (q-tip or other applicator), and let it dry. Then you apply some more again to let it soak into the spots that it may have missed first time around, or you can go ahead and re-tap the threads if you're sure you got it all. If the threads seem to get a little loose, this method can be used to get them tight again as well.
Please note that this method may not necessarily waterproof your wooden parts or protect against normal wear and tear and that abuse will certainly still damage the items. Also please note that if you intend to use this item as a cooking utensil that heat will affect superglue bonds.
