Hydraulics.& pneumatics can be silent; your link is for a "credit card" sized device, so I assume you need very little actual power. A simple solution might be a pair of syringes coupled by a piece of tubing: press one in, the other moves out. For a mechanical advantage use different diameter syringes. If you filled them and the connecting tube with mineral oil you could get very precise/repeatable results.
Alternately, if you only need a small amount of movement, you might consider a solenoid:
http://en.wikipedia.org/wiki/Solenoid .
As far as a "silent" electric motor goes, that's tricky, and a lot depends on how "silent" you need it to be. The first step would be to accurately measure how loud an existing motor is and then acoustically decouple it using as much foam and other sound absorbing materials as space will permit and then measure the new sound level. With this information and some math you can calculate the maximum allowable motor noise level and begin your search for a motor that is quiet enough to suit your needs, but success is likely to be highly dependent on your budget and tenacity.
There are some very quiet BLDC motors; however, a lot depends on how much power you require, and how much you are willing to spend converting the rotational energy into linear motion.
If the device only needs to actuate 1 or 2 times per show, you might consider simply using a "spring" powered motor. These can be fashioned from spring wire (I generally use "single strand fishing leader wire" for spring making, it is cheap and readily available), or salvaged from children's toys or old fashioned "egg timers", etc. You may even be able to use "off the shelf springs" in compression mode to move your object from point "A" to point "B" and then return it using a second, stronger spring. This arrangement would need to be "ReSet" after each use, but if you only need to move it once or twice, it might be a viable answer.
Fish
