One type of mechanical timer you are describing that can be constructed is a hydraulic timer consisting of a spring loaded piston, with a small flow metering hole,inside a cylinder (the reverse of shock absorbers used in industry to dampenimpacts) but this type of device will require careful sealing of the piston shaft and can be prone to leakage of the hydraulic fluid due to wearing of that seal. As long as appropriate materials are used for the units construction the fluid can be water; but, a more viscous fluid is better forlong delay periods and more accurate performance. Generally the spring on such a device is located outside of the cylinder between the cylinder end and the fitting at the end of the cylinder rod; but, for a more compact design the spring can be located inside the cylinder under the piston.
Time delay electric timers use a pneumatic version of this design but the load to close the contact at the end of the stroke; and, therefore, the spring load and piston pressure are lower than you want for your device.