When it comes to a hedgehog it is better safe than sorry. Many accidents happen within 1 mile of the home, so the "isn't that far" method isn't really logical. It's better to plan for "what if" than to deal with the loss of a pet later--the old "one ounce of prevention saves a pound of heartache" deal. If you have the hedgie in a box or a soft carrier and you DO get into an accident, one that you absolutely cannot see coming like someone t-boning you at a stoplight and you can't avoid even though it's daytime, the hedgie can go flying across the car and be killed, or get out and get lost--whereas if you had them in a hardsided carrier with piles of fleece in the bottom that wouldn't be an issue. It may be a slight chance, but there is that chance. It is better to plan for the "what if" and hope it doesn't happen than to have it happen and not be prepared.
One other reason for a hard-sided carrier is that emergency personnel are trained to look for those carriers, as Nikki said. Otherwise your hedgie might be left freezing at the scene of an accident during winter, or have a heat stroke for the same reason in summer.
A hard-sided carrier runs about $15-20 at Wal-mart and will last the lifetime of your hedgie, and likely the lifespan of any future hedgies you have. A small contribution to give a beloved pet a fighting shot in the case of a "what if" does not cost that much, especially when most people spent about $200 to get their hedgehog in the first place. If you can't afford to buy a $20 carrier, how will you afford vet bills, etc in the future? Of course, can't afford and don't want to are two different things...but how could you not want to when the well-being of a treasured pet is at stake? Most of hedgehog ownership is about prevention--preventing falls, hairs around legs, diet troubles, etc. This is just one more prevention step to keep our companions safe and as healthy as possible.
It's up to you what carrier you use, but there's a reason seasoned hedgehog owners recommend hard-sided ones.
Pixiedreamer, for a 2 hour drive, you definitely need a hard-sided carrier. Any number of things could happen between there and home. Be sure not to put the heat from the vents directly onto the cage--it can become too hot--and use the handwarmers and a few layers of fleece in the carrier to keep your little guy warm and toasty. Warm the car up for a few minutes before you take him out to it, and cover the carrier with a blanket before taking it outside. It's also a good idea to get a thermometer to put in the cage to ensure it's not too hot or cold in there.