Before making your footwear choice, stop and ask yourself this question: "if I stood in a rain storm for 6 hours in these shoes at 0c/32f, would my feet be happy and warm?" If the answer to that question is "no", then you need to bring waterproof boots.
If you have waterproof sneakers but you're wondering about ankle support, this is more of a personal preference, although more ankle support is always better.
Another factor to consider is how many pebbles will get into your shoes. It might sound silly, but 6 hours of walking with constantly getting volcanic rocks in your shoes is miserable--another case for the higher ankle supported boots.
Remember that you can also rent hiking boots. You can see what the rental boot options are like here.