Fish can go a couple of days without feeding (2 or 3). I have had a friend come in to feed them and have left specific instructions about which food (I have floating and sinking) and how much. Do a water change before you leave and they should be ok for a week without water change.
This is general advice since I don't know anything about gouramis, but do have cories.
It is a good idea for someone to come in and check on them in case something in the aquarium stops working or there is a power outage.
Not sure how big your tank is, nor how long you've had your fish, but cories will be happier (not as shy) in a bigger group (around 5) and same type. I have 5 cories (4 cory aeneus and 1 bronchus splendans). The one different one was an oops since I got my common names mixed up (green vs emerald corydora) and didn't ask for the proper name. But he does seem to be ok with the others.
