You need do nothing to the current settings as avast only checks for program updates and if one is available it 'Asks' if you want to download it then. If you are busy and you don't, ignore the pop-up notification and it will go away after a short time. You will then need to do a manual update when you are ready.
This works fine for me, as I'm also on dial-up.
I wouldn't advise downloading the whole new program version (currently about 23MB) as that would be much larger than the program update from within avast.