Option 1: Put the file on my (Android) phone, connect it to the desktop computer with the USB charger cable, copy it over MTP (no drivers needed).
Option 2: Use a USB flash drive or another mass storage device (can usually be borrowed).
Option 3: Forward the file as an attachment to a disposable email account and login to that account on the desktop computer to download the file. (Would not log in to my primary email account or any other sensitive service on the shared computer.)
Option 4: Put the file on some cloud storage service (such as Google Drive) and make it publicly downloadable.