By mid-June, it will be somewhat unpredictable. If you stay on the well-traveled trails, there will be a muddy/icy foot track, and you can probably stay up on the surface most of the time. As you get off into the less-traveled trails, the snow will be unstable, and there will be lots of runoff. Also consider the orientation of the trails with respect to the sun direction and tree cover.
I can guarantee that the top of El Capitan will be bare and dry, but the trails through the woods on either side may be a complete mess.