Exim: Redirect mails without spooling

I am running a personal mail server using exim that only forwards mails (and also runs a few mailman mailing lists).

Unfortunately, my server’s spam protection is worse than that of the mail provider I forward most mails to (mailbox.org). So my server might accept an email, try to send it to mailbox.org’s MX, that will reject it, and now my server might generate a bounce message. Which then often can’t be delivered and would then be frozen.

Can I configure exim to try to forward the mail before finally accepting it, and if the downstream server does not like it, simply reject it as well, so that my server never creates bounce messages in that situation?