Is there a smoke generator that can make strong puffs like this? I know there's a number of smoke machines that create some exhaust smoke, but not short and sweet like this skyline's

you could potentially do that if you find a battery powered piezio electric humidifiers that vaporize water as those can let out a pile of water vapor to where it looks like smoke, but it will most likely be pretty bulky as you will have to have the device, and a water reservoir.
There are also parts from henglong smoke, and sound tanks that might work which use a few drops of (I think) castor oil to make smoke which are essentially just a resistor that heats up, and burns the fluid, but those won't do anything like that pic.

One of the best ways would be to use a e-cigarette.... they are tiny and put out massive amounts of "vapor"

there is a few videos around on how to modify them, but its not going to be under pressure like a NOS purge, so u might not get the desired result

actually..... the best way would be to use a refillable cigarette lighter tank.... but lol, i dont know if i wanna recommend that, it could go horribly wrong... maybe check out some rc submarine forums to see how they use those tanks and it will give u some ideas