Update
I should have mentioned - we are going on a wildlife photo trip that will involve the monkey park at Jigokudany then on to Hokkaido, staying in Rausu, Lake Kussharo and Tsurui.
The hotels we will stay at have no internet access, according to the tour organisers.
Looks like there is no wifi coverage with the device I mentioned above in those areas, so I probably will not rent one.