We stayed at Ashford, and we made both our School of Falconry reservations and hotel reservations about a month or so before our trip to Ireland (late August about four years ago). But, that was before Ashford Castle was named one of the top 5 hotels in the world (under its new owners) and underwent a huge renovation (and it was absolutely lovely before that). Unless something has changed, the school accepts reservations regardless of whether one is a guest at Ashford or not.
We had a guide just for the two of us, and we each had our own hawk to learn the launching and landing techniques. We had a short orientation before taking to the garden/forest, during which we learned about hawks, how they live, how they feed, etc. Very interesting.
We also observed the hawks being readied for other guests at Dromoland.
The advantage of doing the Hawk Walk at Ashford is that the grounds are vast, so lots of room for the activity. But, likely, you would have a nice experience at any of the places you list. We did not stay at Adare Manor (we just dropped by for coffee), but it looks truly lovely!
If you have not already searched YouTube, there are lots of postings of people enjoying the experience. Definitely fun and memorable!