I'm not sure how large the blinds are, but you can try wrapping a pair of salad tongs with microfibre cloths and elastic bands. Grab each slat with the tongs and drag them across to remove dust. You can also dampen the cloths with warm, soapy water if the blinds are a bit more dirty.
Been there myself. I had to fill the tub and soak half at a time. Try the floor wax after you've found yourself a way to wash them.
Unless they are extremely dirty, purchase a good microfiber duster that catches & captures dirt and dust. Then you can run it over the blinds. Growing up, my mother made me clean ours and I used a butter knife covered with a dusting rag that was sprayed with something similar to Endust. I also had to do the louvered doors. UGH! You could use tongs with a similar mode if they are very dirty.
The blinds are almost5 1/2 Feet long and there are stains on them and yellowing from the sun. Hard to find a tub that will fit them. Thanks
Difficult but if you can put them in a bathtub maybe with T.S.P? Once they are dry, I would rub some future floor wax on them, it makes dusting them so much easier. This also works on ceiling fan blades.
I should add that the floor wax prevents the dust from sticking in the wood surfaces.