We got tommee tippee instant milk modular and use the water for cleaning her face and bum with cotton balls before bathing and changing into pj So I guess your way of boil-let cool-store in thermo flask would work too!
I used normal tap water. Baby was fine. if u see tt baby's skin seems more sensitive, u can try sterile water. Aft bathing, just make sure you dry the stump.
I just use tap/water dispenser (warm). No issues on baby’s skin.