How harder the cleaning needs to be done depends upon the quantity of the dust on the slats. If there is a small coating of the dust then simple dusting across the slats will help to keep the blinds clean. You can use the damp cloth to remove the dust. This will not blow the dust in the air as settle on other furnishings.
You can even use white vinegar and cotton gloves. Wear the gloves and dip your hands in the vinegar and squeeze out excess vinegar. Then roll your hand across the slats to remove the dust
For fabric blinds you can use a dry sponge to remove the dust and for metal or vinyl blinds you need to take them off and lean them. Prefer placing them between sheets of towels to avoid scratches.
For extremely dirty fabric blinds prefer giving it to the dry cleaners for the cleaning.