As others already said, mixing colored materials can create hard to predict results. The simplest case is that the printed colors and the wood do not affect each other at all, the yellowing is only the product of filtering effects:
- The white light is filtered (removed a part of it) when the light travels through the printed ink dots
- The wood reflects a part (less blue than others) of it back
- Printed ink dots filter the reflection
In RGB color terms some B is missing, so you could in theory compensate by increasing it in the original photo. You seemingly have already thought this and you only search some confirmation and hints how to make it in practice.
Unfortunately there can be areas where the B is already in its maximum, for ex. all white areas, so you can only increase the percentage of B and you should do it by reducing red and green. This will reduce the available contrast and your image will look underexposed.
We can try what you could get at best with this idea:
On the top I have an image of wood (a random capture from a webshop inventory, unfortunately not the same as your wood). It has got blending mode Multiply to simulate filtering. In the bottom there's a random sports news photo. The result is heavily yellow as expected. It has also poor contrast, because the wood removes tens of percents of the light. White paper would take less. The photo is, of course, at first adjusted to a printable color range by converting it to CMYK with relative colorimetric conversion intent and then back to RGB.
As said by others a compensating adjustment layer can be used. It's inserted in the next image:
Red and green are reduced, blue is the default. The resulted color is nearly neutral in the lightest areas of the wood texture, but the contrast is poor. This very likely cannot be accepted when one tries to make attractive toys. The contrast would be better if you can accept white areas to become the same as the wood. Then you can increase blue.
Just for a comparison: The right half of the next image has the original (after making it possible in CMYK) photo colors and the left half has the assumed blueish precompensation which is made by reducing red and green. The wood layer is closed.
My suggestion: Try to find a way to make the wood closer to white - a white underpaint or chemical treatment. Unfortunately I cannot tell a working method which will integrate well to your workflow and cost expectations and doesn't interfere with the printing. People who print on canvas have the same problem, so it's possible to get some hints from there.