I walked the Baztan two weeks ago and did the same itinerary that you mentioned. It was hot and dry on the first day and cool and wet the next two days, followed by a warm dry day. Unless it has been raining torrentially for quite some time, there is no problem with mud. You dont need waterproof shoes for this route in summer. I used my normal summer hiking shoes. They got wet in the rain and dried overnight, or in the sun, as I walked, without any problem.
I suggest you use your normal hiking shoes. May be your blisters are because of wrong shoe or sock sizes or a combination of both?
This is what I do for blisters:
If I note friction or hot spots, I stop and use plaster (esparadrapo in spanish) to protect the zone from fruther friction. If I note it one day, I tape over it the next day before I start walking. This time, I got a small one from the wet socks. Noted it right on time to apply the esparadrapo. No problem from then onwards.
For the poles, try contacting the hostal you plan to stay and see what they say.
Now, a bit on my experience:
On the French side, the way markings are discrete and were missing at some places. We were three walking on that day and all three got lost at some point. This is somehow compensated by the excess of yellow arrows in Spain. So, better to have a GPS track with you, just to make sure on unmarked intersections or when you are in doubt - there is no need to follow the GPS all the time.
First day from Bayona to Urdax was a bit hard due to the hot weather and asfalt. Follow the riverside walk until you reach Ustaritz. There are water fountains in some sections. But make sure you carry enough water from Ustaritz beucase there are not many water fountains in the french part. If you want to eat something, or refill your bottle, you have to go to Espelette or Souraide. There is not much shade in this section after Ustaritz. So, hot weather makes it worse especially near the col de "Piña colada". In Urdax, there were a couple of bars and a food truck open till 8. So, you can eat some pintxos, etc., but please check their timings, as soon as you arrive.
The second and third day were hikes in beech forests. We were lucky to have nice cool temperature and slight rain (a slightly heavier version of Sirimiri). You can have lunch in Arizkun or in Elizondo. Also buy food for dinner and breakfast from Elizondo, as there are no shops/bars in Berroeta. The restaurant in Lantz remained temporarily closed. There is a shop in Olague which closes at 14:30 and opens again in the evening from 19:00 - 20:00 h. The hospitalera in Olague also sells local cheese. There are basic kitchens in the albergues of Berroeta and Olague. Our shoes got wet, but dried at night, but got wet again on the next two days from the wet grass and rain. The Roman road in rain is slippery and I had a small sideways fall due to slipping. Be a bit more careful with wet Roman roads.
The stretch from Olague to Pamplona looked a bit unused and with overgrown plants. If you dont like getting scratched by thorns or are alergic to insect bites, use long trousers.I did it in shorts and ended up with some bites and scratches, which I expected. There is a bar in Sorauren. If you have alrady done the
camino Frances, I suggest you take the riverside walk to Pamplona from Trinidad de Arre. Don't cross the bridge when you reach the village, but continue straight. This path has more trees and shade, but is a bit longer.
In Pamploa, we found that trying to have lunch is a bit complicated without previos reservations (also, we arried at the peak time :14:00 h). But, we managed to find a restaurant after looking around for some time.