I'm going to disagree with those who say you don't need boots for the Ireland tour, especially considering the time of year you're going. I'm also going to say that those Anaya boots are city fashion boots, not at all useful for the kind of tour the 14 day is described to be. The last thing you need is to turn an ankle, slip and fall or have your shoes get so wet that they don't dry out overnight. See the weather averages toward the end of this response.
I encourage you to closely read the daily itineraries and the descriptions of the amount and kind of walking listed at the end of each one. Pay particular attention to those that say, "Strenuous walking: 2–8 miles throughout the day with lots of hills, stairs, and uneven terrain." In fact, the overall info on the tour says, "This is a very active tour! Most days are moderate to strenuously paced with 2–8 miles of walking, including hilly terrain and lots of stairs."
I highly recommend that you consider some lace-up, waterproof ankle boots that are supportive for the kinds of terrain and weather you are likely to experience on the tour.
I'm not a particular fan of averages, but these are the timeanddate.com October weather averages for some of the places the tour will be. You can go there and research the exact days and locations for the past few years to get more recent data.
High. Low. Precipitation. Humidity.
Dublin: 57°. 45°. 2.06". 85%.
Kinsale: 56°. 46°. 3.85". 89%.
Dingle Peninsula: 59°. 50°. 6.35". 82%.
Galway: 58°. 47°. 3.11". 85%.
Belfast: 55°. 47°. 1.98". 82%.
I'll be on the same tour 24 July to 6 August. On the plane and everyday on the tour I'll be wearing these KEEN Terradora II Waterproof Mid Hiking Boots in the Majolica/Tapestry color. I suspect that these are the kind of boots some people have in mind. REI has them in other colors as does Amazon.
Ankle boots like these have great support and stability for all those hours on foot and walking. They've kept me from turning an ankle or falling on rough or slippery terrain. And, along with my Sockwell socks, they've kept my feet warm (or cool) and dry.
There are lots of good socks and people have their favorites. I like the Sockwell moderate graduated compression ones. They're great on the plane and help to fight standing and walking fatigue. I've never experienced a blister when wearing these socks Plus they come in fun patterns and colors. These and these are my current favorites.