When I prune mature kiwis I just try to leave plenty of the knotty small wood and remove all the big vegetative wood. I also remove the thin long tangling pieces that tend to strangle wood they wrap around. That works well enough to where my plants are solid flowers in spring.

There is always a chance of damage when you prune after the plants leaf out, but that does not mean it will always cause damage. I have pruned many trees vines when I shouldn't and no harm came. Vines will bleed a lot, but will stop. Mother nature often prunes plants with wind, hail, animals and they still make it. I sometimes prune my grape vines after they have set grapes to add size to the grapes. I prune the vines in the winter anyway and a lot of what grows is going to be cut off anyway. You said you have plants that look a couple of years old. Does that mean you don't know for sure or maybe someone else planted them and you bought the land or something. If they have never made fruit, then maybe ther is no male vine. I would agree with the desired vine form. All mine are straight up to at least 6 feet with a single vine. Then I prune in the winter to control shape, growth and vine size. Just like many plants the growth can be to either make plant or fruit depending on how you prune. If the vines are a couple of years old they should be at least 1 1/2 inches in diameter, and already have a single main trunk. If not you have a mess and should try to get a single trunk. I assumed that already was the case and did not feel it worth prunning until winter.

this is a great link for hardy kiwi growing http://extension.oregonstate.edu/catalog/pdf/pnw/pnw507.pdf Here is a link that might be useful: Growing Hardy Kiwi

I have a couple hardy kiwis that I attempted to get under control last year. I cut the vines way back and before long they were huge again. It was around the same time of year, give or take a few weeks.