Sure you can. Vestments worn by priests are washed, as are all the clothing worn by Religious Brothers and Nuns. I am a secular Carmelite and can tell you that I hand wash my Scapular at least once a month. I treat it with reverence each time I put it on, kissing it and saying a prayer to the Blessed Mother.
It would be no different than cleaning a blessed crucifix you wear around your neck. It’s not the “item” you wear, but the comittment you make by wearing it.
In His Peace!