I take them down put in bathtub and spray them with spray nine then use s soft bristle brush rinse looks like new
Dawn soap does wonders for cleaning grease and grime. I would try that first. Murphy’s oil is made specially for wood too. Put a fuzzy sock on your hand, wet the sock with the dawn and water solution and then run your hand through each slat of the blind with the sock on. When you are finished - throw the sock in the wash. Easy peasy!
Krud Kutter may do the trick. Just make sure you get the stuff meant for cleaning, and not the stuff meant for paint-prep!
Wear a sock or
Wear a sock or cotton glove on your hand and wipe dust off first than add dawn dish soap and warm water in a bucket to tackle the grease using a sponge then once dry spray with wood polish so dust/grease/grime will repel.