If he is busy and cannot come for 10 DAYS to replace the old pipes that have completely closed up and refuse to swallow even a drop of water....
If you cannot run your dishwasher for that entire 10 DAYS because it uses the same clogged pipe that refuses to drain...
If your sink has filled up again with the few dishes you own that are not already sitting dirty in your dishwasher...
then you should definitely fill a large bowl with soapy water and start washing. BUT {and here's where the water saving plans come in} make sure that not even a drop of water goes down your drain, so do NOT turn the water on full blast. A trickle will have to be enough.
AND...when that bowl of water gets filled with dirty-dish water, then dump it in ANOTHER large bowl...which you will need to promptly empty outside in the flowerbeds so that you can refill it again. {But be sure to dump in multiple sites, lest you should end up with water in your basement.}
When you have accomplished all of this AGAIN...stack, the clean dishes in the neatest pile possible to drip- dry. Don't even bother to put them away, because someone in your family will be using them again in a few mintues, and you'll need to start the process over....AGAIN.
While you may not like it, get used to it...you have just managed to save a few dollars on your water/sewer bill. And, perhaps you will have a greater appreciation for women who have to wash their dishes like THIS every day....