That's a SWEET price for Ertl pump in a box!
I think the squeaker could last for some time if it is not depressed with a sharp metal object, maybe something like a dart gun suction cup or something soft on your vertical plunger as a cushion?
The squeaker will likely make good water pressure on the down stroke, I am unsure if it will have a lot of strength to draw in the new water so a check valve with very easy open strength will be needed. Are you going to make your own check valves?
Keep us posted if you make any progress.
I see the edge of a Tarot Stirling engine...nice choice! I have one on order myself
