Personally I would go with poles and one ice-axe as long as possible. As soon as there are have prolonged steep slopes (defined by having to ascend with front points of crampons) I would take two axes.
I originally wrote the paragraph below assuming it was mountaineering (in May - silly me). It is still relevant and applicable, but it assumes that a pole is an additional item. As you have one (two) anyway for skiing, the threshold is much lower for exchanging one ice-axe with a whippet. As I have no experience at all with whippets, I am not really knowledgeable to advice on its usage. I will delete this when more complete answer comes up.
If you go with the worst case of your requirements, it is clearly two ice-axes. In hard frozen snow or ice in a 60deg slope you will be ascending using the front points of the crampons and both ice axes with picks in the snow and hands on the shaft. In snow that allows to create good steps, you can ascend upright zigzagging in slopes up to 60deg. So really it is a judgment call, so you should go with what local guides recommend.