"Or just whip them into the dishwasher."
I would reccomend avoiding this. When I pull stuff out of a dishwasher, the items smell clean, which means they still have residual substance on them like JetDry. Fish certainly will not appreciate the soaps from a dishwasher.
I clean my plants by boiling some dechlorinated water, then I grab the plants with tongs and dip them in the water for a few seconds.