Hello anonymous user and welcome to Microsoft Q&A.
Ideally, the things you want to migrate would make up the collaboration branch. The collaboration branch is like a master branch, as is what gets published from.
As you only want to migrate just a couple changes, this sounds similar to a hotfix rather than a normal update. Read about the hotfix approach here.
There is a way to publish triggers. However, do note that triggers cannot be updated while active. There is a script to stop-start triggers here.