In Windows Explorer, in Details view, what does it say alongside .NTF files
in the File Type column?

In Windows Explorer, Tools > Folder Options > File Types tab, scroll down to
find and select the NTF extension, and click on the Advanced button. Click
on Open to select it, then Edit. What does it say in "Application used to
perform action" and the other fields, if "Use DDE" is ticked?

A few more random suggestions:-

See if you can extract the particular version of odbcint.dll from the
installation media and copy it to the directory where the Neato executable
is located.

Try reinstalling the program in Safe Mode, see if that dll is still locked.

For a possible workaround, try adding a shortcut to your Neato program to
your Send To files, and see if you can right-click Send To... on an .NTF
file from Windows Explorer. Not a fix, and rather clunky but it might do it
for you (suspect it might not work, anyway).

Try creating a shortcut to open the .NTF file with Neato, that in the Target
it reads:

C:\whereveritis\neato.exe c:\wheremyfileis\darnedfile.ntf

NB: if there are spaces in either of these paths, enclose the path in speech
marks, thusly:

"C:\Program Files\Neato\neato.exe" "C:\Documents and Settings\Fred
Flintstone\My Documents\darnedfile.ntf"

Would it be so terrible to have to open the program first, then open the
file from within the prog?