We are carrying out a research experiment in which we would like to keep squid for a few hours after catching them. We have been told that keeping squid is almost impossible in the long term because of their boundless energy, but do you think it would it be feasible to catch them, place in a saltwater-filled bucket for transport, and then into asmall aquarium for 3-4 hours.

I have caught small bobtailsquid and they were active for a few hours after catching them, they survived about 12 hours in a very shallow viewing tray.
I think any squid you catch is definately gonna die - but they should survive for a while. I havent ever seen a squid bigger than a few inches alive - but I'm geussing they'll be similar.

How about a small kid's pool instead of an aquarium? That way, they might make it back to the sea alive...though doubtful at best.

Success will depend entirely on the size and species of squid. Don't transport them in a 'bucket', but in a bucket with a large plastic bag liner that is firmly tied at the top; this will prevent a lot of sloshing. If you have access to an oxygen cylinder, squirt a good dose of this in there as well, prior to adding the squid; it would pay to remove most of the air within the bag when actually sealing it (further minimising sloshing during transport). Put the lid on and keep it in a cool and relatively darkened place.

The 'small' aquarium also will need to be round to keep them alive for a few hours, and preferably non-polyethylene.

I've heard that putting a light onto the top part inside of the container also helps. No proof, but that's what the fisher-folks do at the dock.

And we need a "squid care" sub topic.

I would put them in an ice-chest as long as you can get then home in under an hour you should be fine. Buy a small battery powered air pump to oxygenate the water with. A lot of the success with keeping squid is having the proper tank. You will not be able to keep them long in a regular aquarium unless in is 6 feet long. The other main problem is that they only accept live food (fish) and they prefer certain kinds, silversides seem to be one of the favorites around here. They need to be feed everyday if not they will start attacking each other. Overall it is not impossible I've keep squid alive through the entire life cycle, the main thing to focus on is the tank and food.