A wee note of warning regarding my original question of plugin-less domain mapping. Plugin-less domain mapping worked great until I had to conduct a network upgrade of all my sites (the standard wp process that updates all sites after a database change).
One of the sites on my network had an expired domain and this resulted in the network upgrade process stopping once it reached the site with the expired domain. To finish upgrading my network I had to revert back to a plugin-based domain mapping solution.