For clay pots and short periods of time, you could think of using capillary matting - one end goes into a trough of water, and you stand the pots on the matting. Water is sucked up by the capillary matting and the clay acts in the same way to keep the pots damp. You ill need to experiment a bit , to see what sort of supply you need in the container etc, and sit the matting on a sheet of plastic larger than the mat, otherwise water will keep feeding into the mat and dripping out of the free edges.
Mounted plants are a bit more difficult ; in the past I have made elaborate setups using timers , a pump, and spray jets, but home-made installations like this - at least the ones I lashed up - don't work very long before something goes wrong. Maybe the best answer for a short period like a week is to move the plants so that they are well shaded, give a specially good soak before you go, and the same when you get back.
I gave up mounted plants when I first retired from work and was away for 25% of the time seeing the world, and as we say in UK "ski-ing" (spending the kids inheritance) - it was just a waste of money trying to grow them, although potted plants were OK. Now, much older, and quickly bored if I am away from home for very long I grow them again - and get in hired help to spray them only if I will be away for more than say 5 or 6 days.