This is more a sys admin issue, but being one as well, we normally use high end replication systems, but this likely is not an option.
The best thing to do is actually suspend the store, let's say at 2AM,but your time should reflect the lowest visitor time. Then perform your migrations and then restart everything when complete.
There really is no valid way to reintegrate any changes, however there is a way to do it, simply by exporting all queries (made by MySQL), or filter only the INSERT, UPDATE, DELETE ones, and reapplying those after upgrade. This can be set inside MySQL but would require a service restart, but then you should have minimal downtime. I do not advice this though, as the upgrades might make queries fail and you will have missing or broken data.
Suspending operations is ALWAYS the best method.
Again, this can really only be answered by having a deeper understanding of your systems, but as is, this would be the way to go.