Slats used in vertical blinds are wider than those in traditional, “Venetian” blinds, making it somewhat easier to wash them in place.
The best tool for use on vinyl vertical blinds is called a tricket, which somewhat resembles a pair of tongs. Sponge trickets have small sponges on both sides, for washing; use squeegee trickets to help dry the slats. They are available at janitorial supply shops.
Dip the sponge tricket into a bucket of water and detergent solution. Close the tricket around each slat and wipe from top to bottom. Repeat with the squeegee tricket. It will be helpful to place a drop cloth under your work and have a dry cloth or two on hand for blotting up any drips.
Reference:
Don Aslett in The Cleaning Encyclopedia: Your A to Z Illustrated Guide to Cleaning Like the Pros.