You can't use a hand pump to pull a vacuum, I quickly found out that as soon as you stop squeezing the altimeter thinks it is at apogee...you'll need to have some thing that will pull a constant (slow) vacuum. I have made a chamber with my vacuum pump but I need to find a chart that will cross reference a vacuum to an altitude...I am afraid of pulling to much and damaging the altimeter...
The best atmospheric calculator is here.
https://www.aerospaceweb.org/design/scripts/atmosphere/
You can't hurt the altimeter pressure by pulling a vacuum on it. That's what it's designed for. You can damage it if you pressurize it substantiallly above atmospheric pressure however. That level is about 2 atmospheres.
A way to simulate a flight to a specific altitude is to have 2 chamber of different volumea connected by a valve. If you pump out the larger one to eliminate most or all of the air, then open the valve, you will simulate a launch to an altitude equivalent to the equilibrium pressure when the valve is fully open. If you then vent the large chamber, you will pressurize the smaller chamber at a slower rate than you pumped it out simulating descent.
The math is pretty simply. The volume of the test chamber is V1 and the vacuum ballast chamber is V2, and the pressures in chambers is P1 and P2, and when equalized Pe which is the atmospheric pressure at the desired altitude.
Pe = (P1 x V1 + P2 x V2)/(V1+V2).
To equilibrate a specific pressure Pe equivalent to your desired apogee altitude, you need to pump out V2 to a pressure
P2 = [Pe x (V1 + V2) - (P1 x V1)]/V2
To figure out the volumes of the chambers you need a digital scale that measures in grams and has a capacity of several kilograms. A liter of water = 1000 cc or ml and weighs 1 kilogram. If you put an empty jar on the scale and weigh it, record the weight, and then tare out the weight of the bottle. Fill the jar with water with water and record the weight of the water added to fill the jar. The weight of the water in grams is the volume of the jar in cubic centimeters. to make sure you have not exceeded the capacity of the scale add up the tare weight of the jar and the weight of the water and make sure it is below the maximum capacity of the scale.
Bob