Both .nsf and .nsh files are databases used by Lotus Notes and it is likely that only this program can work with them. However we couldn't find any relevant information if saving the newer .nsf databases to older .nsh files is actually possible. It all depends on the backward compatibility of Lotus Notes.
Convert Lotus Notes database to Lotus Notes database file.
We found one software available in the database for this conversion.
Microsoft Windows software - convert nsf to nsh on Windows
A multi-user client-server cross-platform application runtime environment for Lotus Domino/Notes suite
Convert from nsf file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.