I would suggest compressing your WAV as an MP3 instead. MP3 is an audio-specific compression format, whereas ZIP is a more general-purpose compression method. Because ZIP is general-purpose, it is less suited to the specific task at hand of compressing audio.
The MP3 compression algorithm is designed specifically for audio, and is a "lossy" algorithm and thus can compress audio far better than ZIP can. ZIP uses a "lossless" method and is thus forced to preserve each and every bit in the recording verbatim, taking up more space in the resulting compressed version.
Even though compression for MP3 is "lossy", such information loss isn't likely to affect the perceived quality of a voice recording at all, provided you compress your WAV file at, say, an MP3 bitrate of 128Kbps or higher.
Your distance education language instructors should be able to deal with an MP3 audio file (MP3s are incredibly common nowadays) but check first to make sure this is an acceptable solution for them.
If compressing using MP3 or another audio-specific algorithm isn't acceptable, you could reduce the sampling rate or other parameters in your WAV recording. If you are recording at 2-channel (stereo), 44KHz, 16-bit, for instance, the file would be larger than if you recorded at, say, 1-channel (mono), 22KHz, 16-bit. etc. Play around and find out what is acceptable for your voice recording.
1why not just upload the file into a dropbox or any other cloud account and send them the link? Or just use the correct way call the School and ask them for further advice maybe you aren't the first one confronted with this Problem and they already have a Solution or at least can tell you what the recommended recording settings are – konqui – 2017-03-24T19:31:36.753