Why not use a cardboard box?  Boxes are cheap and easy to obtain, and often do the job satisfactorily BUT:-
- bees can cling on better to a straw skep than to smooth cardboard.
- If the sticky tape that holds the box together comes loose, the box can collapse
- if it rains, a skep keeps its shape but cardboard goes soft and bendy.
- it's easy to seal a skep (see below) but not so simple if the bees shut in a box are to breathe and stay cool.
- a straw skep is "breathable" - the air can pass through it so the bees are comfortable. Only when a colony has lived a while in a skep do they seal up all the air passages with propolis for the winter.
- and, of course, if you have a skep you won't have to go searching for boxes in a hurry.
- and it looks so much better from the point of view of the spectators - think about your image.

Suitable shaped skeps.

The traditional domed shape is not necessarily best because it rolls about when placed mouth upwards.  Looks nice but........
Better to have a flat-topped skep for carrying swarms. It sits steady on the back seat of the car mouth upwards as you drive home.

A wide  mouth is easier to aim at when putting a swarm in a skep, so have a wide skep.  A wide skep is also more stable when balanced above a swarm in a hedge so that the bees walk upwards into it.

It's best to carry bees in a skep with the mouth upwards covered with a tight cloth through which the bees can easily lose heat and get air.
Think of it as a drum filled with bees.

If your skep has an entrance in the side you will have to stuff something (grass?) into it to close it as you travel home, but it does provide a good way for stragglers to join the swarm unce the skep is on the cloth.

The cloth for closing a skep.

Don't use a big sheet that wraps up the skep. Better to seal in the bees with a tight cloth so none can wander, but leaving the skep surface exposed. 
In advance, make a special cloth for the job and you will avoid all that trouble getting wandering bees off a big sheet when you release them into their new hive.
1. Cut a square of thin but strong cloth that will let air through (back of an old shirt?).  The square to be wide enough to come about halfway up the skep all round when it is placed mouth down on the cloth. 
2. Now find some strong string, four large nails and four little stones the size of peas.
3. Tie a string about 30cm long to each corner of the cloth, using the stones in the corners of the cloth to tie round so the string cannot slip off.
4. Tie a nail to each string so that when the strings are pulled one by one up over the skep the nails can be pressed through the straw to hold the cloth tight closed.

When not in use the cloth, with its nails, stays in the skep, ready for immediate use.

Modus Operandi  (Latin for "this is what you do...")

Spread out the cloth on the ground under the swarm where it hangs. (You could even use the nails to hold it spread out if it's windy.)
Persuade the swarm into the skep. Hopefully you can just hold the skep under them and drop them in by cutting or shaking a few twigs.
Sometimes it's best to set the skep above the swarm and make them walk upwards into it by giving the lowest ones a whiff of smoke. This is the best way when the bees are in the middle of a hedge or clustered on something solid. It sometimes speeds up the operation if you brush the bees into the skep or dump in handfuls of them as you scoop them off a wall or other awkward place. A bee brush might come in handy for this.
When most of the bees are in the skep, put the skep of bees mouth down centrally on the cloth and either open the entrance or put something - a stick - under the edge so the stragglers can find a way in.
Watch for a little to be sure the queen is in the skep. If bees walk in and turn to face the way in, you are OK, but if they face outward and start taking off, the queen is probably still on the tree or has flown a short way, in which case you have to watch where the bees are clustering and start all over again.
Often it helps to either remove the branch the bees were hanging on or make it smell revolting to them by smearing it with Vick vapour rub or something similar. This is to remove the scent of the queen which may attract bees back to where they were.
When only a few stragglers remain, close entrances and pull up your strings carefully and press the nails into the straw so that the cloth covers the mouth of the skep tightly and securely. You are ready to go!

When you get home, either dump the bees unceremoniously into the top of their new home and put the lid on, or do the traditional thing and dump them in front of the hive on a big board or a cloth and watch them march into their new home. Give the skep a thump to dislodge the last few and shake the cloth. 
Keep the cloth in the skep ready for the next time.