I've got two different kinds growing Kaz - the one I had today is called Femspot and doesn't need peeling. The other one however is really prickly and will most definitely require peeling. It'd hurt your mouth otherwise.
Not sure what ours are, but they are quite short and thick (ooer missus!!) and the skin is thick, and as a matter of interest I find peeled cuke less likely to give me tummy ache