Nice try! The soap will do a good job of removing the 2-cycle spitback oil. However, what does water do to wood fibers? It causes them to swell locking them into the filter!
Put the filter in a warm, dry place like and oven at low temperature for a few days to throughly dry out the wood fibers embedded in the filter. Once the filter and the debris that it contains is completely dry get some non-chlorinated brake cleaner and spray the filter directly with the stray from the inside out. This should remove most of the sawdust. After the brake cleaner dries hold the filter up to the sun or other bright light source and look for light through the filter. Light is good pinholes are not. Pinholes means that it is time to replace the filter with an OEM unit.
Here are some photos of a Stihl 026 air filter
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As Found!
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Light test
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After brake cleaner. All you see is the manila colored filter material.
Please post some photos of your filter.