Robert is correct, just install 8.5.2.1 Traveler over your current install, after upgrading your Domino server to 8.5.2.
Your plan to upgrade the server is a sound one. If all goes well, and it almost always does, you should be done with the upgrade of both in about 30 minutes. Probably less.
It is exactly as you described in your original post. Take down the server, run the Domino 8.5.2 installer, bring the server back up. Total elapsed time will be less than 30 minutes.