I would have a go at implementing this.
When emailing vouchers this currently gets saved in the comment field, so it would be possible to read the email address from there. However I feel that's not very clean and was thinking of introducing a howshared field or similar, that other plugins could also potentially use (e.g. one could imagine a plugin sharing vouchers through a messenger or social media).
Then maybe the resend action could be made into a signal that plugins can subscribe to, to allow plugins to resend a voucher via some other means. Not sure if this is over complicating things though. What are your thoughts @raphaelm? And would you accept a PR for this?

Doing this pluggable indeed sounds a bit more complicated than necessary. I see how this could be useful, but since we only allow sharing by email when creating the voucher, I think only supporting email when "re-sharing" it would also be good for now.

So would you be OK with parsing the email address from the comment field?

No, I think we can afford a recipient email field or something like this on the voucher model :)

When resending the voucher it would be nice to reuse the same message that was sent the first time. The message is not saved with the voucher however, but in the log. What do you think of getting the message and recipient from the voucher's log entries? This would also remove the need for a recipient field. I feel a little bad about abusing the log as a form of data storage however (but then the sendmail plugin already does the same).

Meh, parsing the log really doesn't sound clean. Storing the full message in the voucher model also really doesn't :( I'm a little bit out of good ideas here, but even without storing the text it would be a start.

Probably an own issue, but what about templates for emails? I think this would be even better than just sending exactly the same mail again, because the information in the original mail could be outdated when resending the voucher.