A back pack sprayer won’t be wasted Paul, all you need to do is run water through it after using Chems, it’s then good to go for pure water as well.
I use a gardiners backpack and spray either ubik, sodium hypo and fairy depending on the state of the gutters. There’s never been a problem with staining or a problem with the backpack. Just make sure you rinse it through thoroughly and you’ll have no problems with the pump or pure water use after.
I use an old facelift Phoenix pole with a fan jet on the end of the 5mm hose to spray the gutters.