Guessing won't get you too far.
The air motor has a big plastic piston inside. This plastic piston pushes a very slim, spring loaded, metal piston. This piston pushes the oil the same way the other hand pumped piston does, only faster.
An electric motor would need to move an oil pump (with attached oil tank), which is usually attached directly to the motor, and that oil pump the would feed oil to a bottle via an hydraulic hose. So you would have to fabricate new mounts for the bottle.
As I understand, you don't seem to want to use the air compressor to raise the bike, but in the end, it is going to be much cheaper to raise the bike with the foot pedal.
Below see pictures of an Omega air pump, similar in function to your pump. Also see an electric powered lift table, similar to what you want. Also, see a typical AC power unit with built in pump and reservoir. Also see a single acting cylinder needed to complete the conversion. The ac power pump, the lift table and the cylinder are from Northern Tools. Of course, you will have to shop around to find the parts that suit your particular conversion.