Formaldehyde in plywood and osb harmful— allergies & potentially cancerogenic.

I’m sure your allergy is real. I’m also afraid it’s a bit more complicated than “plywood bad, wood good”.

First, formaldehyde free and phenol glues in wood products are probably more prevalent than you think. it turns out that HPVA and soy based glues are often cheaper than formaldehyde based glues. Purebond ™ ply is formaldehyde free. You should ask your supplier for an SDA datasheet, which they must by law provide for all products sold. I know there are formaldehyde free birch ply panels made in Sweden. I think you have to find actual lumber suppliers who know their products. A clerk in a box store won’t be much help.

Although phenol glues are made with formaldehyde, it’s bound in the glue and they don’t outgas it unless you burn it. https://www.kemi.se/en/rules-and-regulations/rules-applicable-in-sweden-only/swedish-restrictions-and-bans/swedish-rules-on-formaldehyde-in-wood-based-boards
But it also contains Polymeric Diphenylmethane Diisochyanate, which is itself toxic. So the high resin content in OSB probably precludes it’s use. I never used it anyway as we considered it a substandard product strngthwise.
Plywood uses less of it, the free formaldehyde goes away quickly, and here in lumber country ply isn’t much more money.

Second. EU and Swedish law require that all wood based products must pass the E1 emissions standard and must be tested to emit less than .01 parts per million immediately after manufacture. That’s three times lower than the .03 ppm the US consumer product safety commission link you posted says is safe and ten times lower than the .1 ppm the link says is of concern and noticeable. It may well be that the way plywood makers there comply with the law is by not using formaldehyde glues. And as you state, most outgassing is right after manufacture.

With recommended air changes I doubt any health risk have been established at the low .01 PPM level. Fruits like apples, bananas, grapes, and plums; vegetables like onions, carrots, and spinach; and even meats like seafood, beef, and poultry contain and outgas formaldehyde. Even humans “outgas” formaldehyde. It’s a natural part of digesting certain amino acids. If your allergy is acute, don’t eat or have those foods in your house.

Third, natural “ untreated “ wood products on the retail market are often treated with substances as toxic and volatile, or more so, than formaldehyde, including saw lubricants, pesticides, benzine based fungicides, and glycol dessicants and water replacers to lessen shrinkage. These are usually applied as a spray or by dunking when the wood is cut.
The fungicides include didecyldimethyl ammonium chloride, 3-iodo-2-propynyl butyl carbamate, azaconazole, borax and 2-(thiocyanomethylthio) benzthiazole. have fun looking those up. Borax is a common bug poison.

I suppose you could forego the treatmemt by buying at a small sawmill but some fungi in wood can be quite harmful and is the reason they treat.

Fourth, natural woods outgas all sorts of toxic substances as a product of processing and decay. Certain woods outgas formaldehyde and harmful resins, benzines, and even cyanide. I didn’t know until I moved to the pacific NW that I am allergic to the outgas products of Western red Cedar ( resins, formaldehyde and cyanide) and Hemlock ( fungi from the tree, not the toxic parsnip-like plant.) Both are quite common woods out here. Check a wood databases or google for the wood you contemplate using. Some woods also contain high silica content so breathing in dust from them is quite harmful.
The hazards for harm from the product worked with power tools, for example, are more recognized than they were.
Of particular concern for toxicity are most cedars, maples, acacia, and walnut. Of course pines affect some people. Laurel and Black Cherry can emit cyanide and cherry is my favorite wood. I use them all anyway. Ventilate and wear a mask if you make dust.

I’m not saying your concern is groundless and that you don’t have a sensitivity above normal, everybody is affected by formaldehyde at some level. But all wood processing and use has its risks. It is more complicated than you stated.

@Zeppos kindly provided a link to the evidence behind his concerns, and as US federal authorities and agencies often are quite transparent on the backgrounds to their conclusions (FDA being positively outstanding when compared to its European counterpart), one can evaluate the robustness of the data behind the conclusions drawn by the National Cancer Institute on the carcinogenic potential of formaldehyde: and conclude that it is weak.