These steps worked for me:

1) From Command Prompt, type in “regedit” (open the registry editor)
2) Navigate to HKEY_LOCAL_MACHINE > SOFTWARE > ODBC
3) Right click – select Export, and save as filename such as ODBC_Registry_Settings_from_machine-xyz.reg
4) Copy the file to the target machine, and double click the file.

Not sure if:
1) reboot is required, I can go to AdminTools/ODBC and see the changes immediately after running the .reg file.
2) changes overlay or add to what you already have on that machine.

Probably writing some WMI code is a better idea – but I didn’t have time, and in my case, it was a clean machine that I was targeting.