If you want to use the built-in upgrade mechanism, then unfortunately there no way to schedule right now, nor to trigger an update. However, if your server patching is automated using any automation tool, you can just reinstall the agent using the version you want and it will upgrade automatically. (Autoupdate will be disabled in Dynatrace).
Updating the agents during business hours will not normally pose any problem as there are checks to avoid disruptions.
The only problem I've already seen at Clients in addition to auto updates is lack of space. They always have problems with space in opt directory so some agents needs still manual update. Using new binary version needs process to restart so this part can be done during next maintenance window.
Some of our clients has auto updates, some we manually check after each update we know and we are forcing DT to make it. It would be nice option to correlate updates installation with maintenance windows configured in Dynatrace.
For now what we do at our organization is we pull the most recent version of the oneagent the Friday before Patch night. We have multiple environments so we download and save the Linux and Windows installer to our SAN in the event we need to roll back or use an old install version.
When patch night arrives I typically log into Dynatrace 2 hours before we start our reboot tasks and turn on the automatic updates. The updates run and push the latest version and in the following hours they all get restarted.
The following day we go back into the settings and turn off automatic updates. It would be nice to schedule them and say the 3rd Sunday of every month, but for now this is our process.
This is also something that we are looking for. We would very much like the ability to schedule the install. We schedule our automated patching for a weekend and we would very much like the ability to schedule the dynatrace updates to coincide with our patching schedule. Sure I can log in and select update at earlier convenience, but it would be better if I were able to schedule this.