Puffers are just like any other fish......they really won't starve in one week.
Aside from any small fry, or saltwater fish like seahorses and anthias, there aren't many fish that will be harmed from the lack of food for one week. Don't forget too that if you have any algae at all in your tank, that's food for many fish. Plants may be nibbled on by others, and some will search for any lost tidbits in the gravel.
Longer periods of time will of course mean getting someone in not only to feed the fish, but to also add top off water if needed, check the filters and heater to make sure they are all working and to make sure nothing has sprung a leak. Then it's best to leave detailed instructions and a phone # where you can be reached!!