As long as the version on the server you are migrating to is a higher minor version then you don't need to upgrade the current server. Since you have 16.1.6425 on your current server then installing 16.3.6897 on the new server and migrating your data to it should go fine.

Just to be certain though I would reinstall 16.3.6897 on the new server once the data migration is complete, just to make absolutely, positively sure that every config file was updated properly (although outside of the web.config I don't think there were any changes to configuration files between those minor versions...but it never hurts to be safe with one last pass).

Best of luck!