The hair is dense but I can’t tell if it is coarse?
I would just do the back with Laser and not the shoulers/upper arm. Even with the back, there is only any point treating where the hair is thick enough but I don’t know if you can convince them. Technically, they should not treat where you don’t want to be treated and reduce the cost accordingly.
As JMISR mentioned, I would start Laser and electrolysis simultaneously if you want to be more or less hair free in 18 months. It’s more than long enough. It’s not about the difference in cost but it’s about what will get you results. £400 might not seem like a lot but if it gets you close to no results then it’s a lot to waste. But let’s say you only do Laser before you go. You can always carry on with the electrolysis when you come back.
Have you followed the ‘Diary of a European Guy’ thread? Even one electrolysis clearance with the right electrologist should reduce the amount of hair dramatically, moreso than one Laser session.