Howdy All,
Thanks for all of the advice.
I got it done. It's not the best job but it is functional. On the whole, it was a good learning experience.
If anyone looking for tips about this project finds this thread, here's my advice after you listen to all of the previous posters:
1. Drink plenty of water and hit the bathroom before you start applying the caulk. Once you start it is difficult to stop because the caulk just keeps flowing out of the tube.
2. Keep something next to you while you caulk to rest the caulking gun. I used an empty box from a twelve pack of coke. It will control the dribble from the tube so you can have that moment to reposition yourself or fix the caulking bed.
3. When you break the seal inside the caulking tube, you only need to poke it once. Don't expect to feel the same kind of resistance from the Sika seal as you do from a tube of standard silicon bathroom caulking.
4. Figure out how many tubes you think you'll need. Take that number and multiply it by at least 1.5. Now get that many tubes. Maybe add a few more, just to be safe. It is much easier to return unused caulk than run to Home Depot mid-caulking to get more. Twice.
5. Plan to take the rest of the day off after. This is more tiring than you think.
Happy swimming everybody!
ETA: 6. Have a bucket of very dry sand available to make dams if there are any low spots created by joints between coping tiles or expansion joints in the pool deck. I used play sand for this. I also made a dam in the joint at the very beginning so the caulk had something to self-level against. By the time I got all the way around the pool, the caulk had firmed up enough that I could gently brush away the sand dam and complete the job.