Which bitcoin wallet allows me to generate and export a large number of addresses?
It is not necessary to download blockchain to generate address. Use an HD wallet like electrum, so that you can regenerate wallet using seed even if you lose private keys.

To generate addresses http://docs.electrum.org/en/latest/faq.html#how-can-i-pre-generate-new-addresses
To export addresses use electrum command line http://docs.electrum.org/en/latest/cmdline.html