Use no toil filters and no toil oil. Biodegradable and washes up with this special detergent, no toxic crap to deal with. Get a brand new filter and use it from the get go. If a filter has had any dino oil on it before, you can't use No Toil.
It wouldn't be as easy with a C10 filter as it's built into a frame. Dirt bike filters can be removed so you have only foam in your hand and then are easily washed. I love the stuff.