To be completely honest, I would let him be at home in his own tank rather then go through all the trouble and stress of transporting your betta to a new location with all new water to possibly sit in a smaller container, unheated, for a whole week and then have the make the whole trip back home again. Its not really quite like bringing your dog or rodent on a family trip, its a bit more like taking your indoor cat with you....just something you don't want to do for a short family vacation. IMO, a few nips on his tail is going to be a LOT easier to deal with as opposed to all the prep and hassle of transporting him with you.
If you feel like he really gets bored and nips his fins while you're gone and you're positive you have no sharp decor or plastic plants in his current tank, what you could do is surround his tank with some colorful objects....action figures, small stuffed animals, other random little objects you can find...or even move his or another tank nearby(maybe a few feet away)so he can see some movement and not get bored.
You could also get some plastic craft mesh at the craft store and sew a small piece in a circle with a little cotton string or some fishing line to make a tunnel for him to swim in and out of, or perhaps get him a new silk plant or two or a cave to explore while you're away to keep him occupied.
So, there are a lot of things you can do without going though the whole hassle of taking him with you, which could be quite stressful on both you and him. You want to enjoy your vacation I'm sure, get out and go do things, not spend most of it worrying over your little guy. ;)