Hi alpharalpha,
Both covers would be breathable and nice options, with the 4-way being a bit more contouring.
Wool is among the best temperature regulating materials but I would also keep in mind that it regulates temperature in both directions (it’s used in the desert and also in cold climates because of this) so while it may not feel “cool” … it generally doesn’t feel “hot” either and it also helps to regulate moisture (which can trap heat) and reduce the perception of temperature that comes from higher humidity levels (similar to how temperatures feel cooler on less humid days than they do on more humid days). Wool stores moisture inside the fiber itself so it’s very resistant to mold and mildew and this isn’t something that I would have any concern about with a mattress cover that has quilted wool covered with cotton.
There is more about all the variables that can affect sleeping temperature in post #2 here.
Wool allergies or sensitivities are generally contact allergies or sensitivities and it would be unlikely that they would be an issue in a mattress. There is more about wool allergies or sensitivities in post #2 here and in post #4 here .
There is some good information about wool on The Wool Gatherer site here.
Phoenix