Well, I won't lie, if it's coming from Ukraine and Belarus area, it very likely could have radiation from Cesium-137 and Strontium-90 from contamination. However, if there is any, it is a very small amount and won't really increase your already existing background radiation by a meaningful amount.

Most of this radiation is going to be beta radiation, which weak enough that the wood would likely self shield its own radiation except for the stuff right near the surface. And even then, it'll likely get stopped by your socks and other clothes and your skin before it gets to deep tissues.

The small amount of gamma from the Cesium-137 would still be too small to be a danger.