The problem with this approach is that you'll be changing the email addresses.
The email addresses [email protected]
and bevä[email protected]
are different email addresses, however much they appear the same.
Making the change you suggest will break email - people might receive the messages, but they won't be able to reply to them.
Your SMTP server that doesn't handle accented characters sounds like a dinosaur. Much as it might be a pain in the proverbial, replacement and/or upgrade is likely the best solution.
You'll likely be able to get more appropriate assistance over on ServerFault.