A hand-operated cleaning system includes an ON/OFF control unit snap-on mountable onto a pressurized container having a valve stem for delivering cleaning liquid. This control unit includes an outer cap with resilient fingers adapted to snap-grip engage and mount the control unit onto a top rim of the container. An inner cap is mounted within the outer cap for ON/OFF helical turning movement so that turning the inner cap in the ON direction depresses the valve stem for releasing pressurized liquid from its container, and turning it in the OFF direction stops such release. A fluid passageway extends from the valve stem through the inner cap to a length of flexible tubing coupled to the inner cap and extending to a remotely-located, hand-held applicator wand. This applicator wand has a fluid passageway communicating with the flexible tubing for providing a path through the wand to its nozzle end. A valve is positioned in the wand for operation by a button actuator. Depressing this button actuator by a user's thumb or forefinger opens the valve for delivering fluid out through an axial bore of the nozzle. A brush is mountable in the nozzle bore so that solvent dispensed through the nozzle bore for brushing application of dispensed liquid onto a surface to be cleaned. The button-actuated valve is spaced away from the end of the elongated nozzle for enabling the nozzle and brush to reach into places of difficult access.