Are these the wooden ones. Or the Metal ones.
If they are metal you can soak them in a bath. 40 minutes with soap, fairy liquid does it.
Then unfortunately wipe each slat with a clothe, or tumble drying sheet. (tumble drying sheet helps repel dust)
People use many techniques,
Brushes, socks, but if you want a real result then the above is best if not outsourcing.
Alternatively get a quotation from an ultrasonic cleaning company and charge for the labour in taking and putting back up.
Dave