I think the best approach is to look at the problem the other way round. Instead of thinking about what you are removing the dirt from, think about what dirt you are removing.
If it is dust from human skin cells (house dust) or blanket or carpet fluff, hoovering with a brush end nozzle should work.
If it is a layer of grease from cooking near the window, you'll need to spray it with IPA and wipe with kitchen roll.
If it is tobacco staining, your best bet is to buy a new blind, but spraying with IPA and white vinegar mixed night help.