For science, CLEAPSS provides model risk assessments and most schools use them; you do not need to reassess every reagent. Cleaning, DT and site maintenance are where assessments are usually missing.
Wood dust in a DT workshop is a carcinogen under COSHH. Extraction on machines, no dry sweeping and RPE for sanding are required, and the assessment needs to cover technicians who clean the workshop as well as teaching staff.
The site manager's store often holds the highest hazard products in the building: drain cleaner, weedkiller, pool chemicals, fuel for grounds equipment. Assess these first.