I have some questions about this video:
I would go with Studs. You will be hard pressed to find chains that fit your wheels and tires w/o scarring up your rims. keep in mind studs can chew up your tires, and if they are not designed for studs (most low profile tires are not), you run the risk of even popping some holes in them. Your best bet would be to get a cheap set of wheels and tires for the trip. tube and stud the cheap tires, and drive across the ice on those. But that is just me. also remember that if chains dont fit properly, they can cause more traction problems than they fix, and your speed and ride are somewhat compromised when they are on.
I have never heard of anything but those pens with erasers work good if you dont press down to hard.
Although I HIGHLY suggest checking out more traditional hybrid or road bikes from your local bike shop. Look for a bike that either comes factory quipped with a rear rack or one that has the frame eyelets allowing for a rear rack to be mounted on the bike. Examples below. One even has fenders - in case of an unexpected rain shower or puddle.
