Thanks--delicata on the menu soon!

Are you sure they are ripe? Looking ripe doesn't mean ripe. I have some that look ripe but I know darn well they are not, and won't be for quite some time yet. But your climate is likely much warmer than mine.
If they are satisfactory to eat now, go ahead and harvest what you want to eat now. The rest I would leave on the vine as long as possible. Despite being a so-called "fall squash" I find Delicatas to store quite well in my unheated, attached garage. Leaving them on the vine as long as possible will delay the time at which they begin to degrade and will allow them to develop the fullest storage potential.

Actually, although they could not be nicked with a fingernail, when I cooked them they tasted fine but could have been sweeter/firmer, so I am not going to pick any more until the stems really start drying out.