We haven't had blinds for years but I found the easiest thing for me to do sometimes back then was to just put them in the bathtub and shower them off. I did want to point out that older vinyl blinds (from the 90's and older) were found to be a dangerous lead risk, especially for children. The lead in them broke down and became part of the dust and then became airborne. Here are a couple of articles about the risks with more information.
Information adapted from “Questions & Answers About Lead in Vinyl Mini Blinds”, California Department of Health Services, ChildhoodLead Poisoning Prevention Branch, July, 1996.
https://cchealth.org/lead-poison/pdf/miniblinds.pdf
And from Reader's Digest:
I am concerned that my venetian blinds may contain lead. How can I be sure that the blinds do not contain lead?
The blinds that you are referring to are cheaply made plastic blinds that contain lead as a stabilizing agent. After the blinds have been in the sun for a long time, the lead in the blinds breaks down and turns into dust. If the dust is touched, it can make its way into the body. Children and pregnant women are particularly vulnerable. Lead can cause brain damage and other serious problems, so it is very important to make sure that you do not own blinds that contain lead. There are government publications that provide informative instruction on what types of blinds (and other household items) are dangerous. If you are worried that your blinds contain lead, you can buy a product called a lead tester. It is a 7.5 cm (3 in.) tube with a short, bristled end. Squeeze the tube, which secretes a yellow liquid, onto the surface of the blind. After mixing it over the surface with the bristled end, watch to see if the color of the surface turns red. If it does, then the blind contains lead. If it does not turn red, then the blind is lead-free. The gadget is easy to use and not very expensive.