Arie Versluis , LinusCansby is correct here, you can't change the setting then go test it. It can take number of days before the routing will properly update, it's something Microsoft is working on improving but until then it makes it hard to do any kind of Migration. The best you can really do is set your org Skype only or skype with collab, wait till everyone is good in that mode, then migrate your stages in batches across keeping in mind that those users will have some lead time on the change over and it's something you can't plan or know turns on and is just something that will kick in when it does unfortunately.
If you were setup Islands then try switching and testing, you won't get any good results. Have to pick one path other than islands, wait for it to converge, then start moving folks. Or use and stay in Islands and make sure everyone knows what they are and install / use Teams and Skype during the transition, then move people to Teams only from there knowing all Chat from Teams will end up in Teams etc. in this mode.