I washed my ties by hand then drip dried them in the shower on a rack.
to gut them quickly fold at seam and rotary the seam right off. They will be very hard on your rotary blade and mat, use an old mat or the backside of one. The little bit of fabric you lose isn't much use anyway.
Yes your fabric will need pressed. I don't know how dry cleaning works, but if I were doing it again, I'd just take them all to the cleaners.