Yes, based on the information provided by Method, you can use their All-Purpose Cleaner on wood surfaces.
According to the product description for Method® All Purpose Cleaner - French Lavender, the cleaner is designed to work effectively on a variety of surfaces.
Product Compatibility
The reference explicitly states that this cleaner:
- Cleans most hard, non-porous surfaces.
- Is suitable for use on surfaces including:
- Counters
- Tile
- Stone
- Wood
- Glass
Therefore, the manufacturer indicates that their Method All-Purpose Cleaner is appropriate for cleaning wood surfaces as well as other common household materials.
When using any cleaning product on wood, especially finished wood, it's always a good practice to test in an inconspicuous area first, although the product information confirms its intended use on this material.