That looks like just the thing that is needed- no tapes and full voltage from the cassette deck amp! (Caution- may not work with the TI if you use a modern retro deck made for modern headphones)
The spec for my digital recorder suggests 70mV to the headphone socket at maximum volume- this is in line with a European standard maximum of 75mV.. Modern headphones are low impedance to work better with a small battery operated devices and obtain high volume at just the low voltage.
This is why your old headphones (or the cheap ones!) seem so much quieter than the fashionable modern ones you have just sold your car for!
I think my old (1983) cassette recorder supplied over 2 volts and was intended to output to the higher impedance or lower sensitivity headphones of the day (anyone have a catalogue/catalog giving the impedance of a 1980s headphone?). I can't find any specs from TI on the audio signal level required or the impedance offered to the tape input.