Performing an 'Advanced Search' on http://canmore.rcahms.gov.uk/ for schools in Harris returned the following list.
Most of these results relate to schools that were marked on the OS 1st Edition 6-inch Map of 1881/2 thus saving me the task of poring over images of those maps online!
(NB - The Six-figure references may not always refer to the precise site of the school)
Steinish (Kyles Scalpay) NG206982
(Tarbert Primary School 1896)
Kyles Stockinish NG13?91?
WEST COAST (1)
Obbe (Now Roineabhal House, formerly the School) NG025862
The majority of these schools were designed by the architect Alexander Ross in the 1870s but the feature that strikes my eye is the concentration of schools in the Bays including, for example, Drinishader, Scadabay and Collam that are only 5 (Golden!) road miles apart. It would be quite possible to make an estimate based upon the 1881 Census records of how many Scholars each of these schools would have contained, but that is one task too far for me to undertake, unfortunately.