For St Hughs Roman Catholic School
I would have thought they would be in the Wirral Archive service https://www.wirral.gov.uk/libraries-and-archives/wirral-archives-service
however they are actually located in the National Archives at Kew for the Department of Education. They have records for 1919-1934 and 1946-1955.
Liverpool Record Office holds records up to 1936 for St Hughs' Central Schools (collective term for the separate Boys and Girls Schools)
Wirral Archives hold some administrative records such as correspondence, records of the acquisition and demolition of Grangefield and later expansion of School. They will also hold the Education Committee meeting records which will have various performance statistics (I may have some of those records here).SOURCE
For Maris Stella School
It looks roughly the same locations for their records as well with the main records at Kew and the acquisition and location change records at the Wirral Archives.SOURCE