Is it rude to sign off mails with a shorthand
(Am also currently working in Scandinavia, have previously been in universities in the UK, US, and Canada.)  Abbreviations are almost certainly fine; but look at what others in your department do.

In most departments, you should be able to see a wide range of colleagues’ emails (thanks to admin lists/announcements, etc).  Look at what they do, and the range of ways they write.  Additionally, note that emails between close colleagues (e.g. within a research group) may tend to be slightly less formal than emails to wider audiences.

You will probably see a fair range of styles.  So long as you are within that range, you are probably fine; you don’t have to exactly match every individual correspondent.  In case everyone at your department writes particularly formally, then it may be worth doing so yourself — but even then, I would be pretty surprised to hear of anyone in Sweden taking offence at use of “Mvh” as a signoff. I’ve received it in emails from students, professors, and administrators, so at least in my department, it’s considered fine for a wide range of professional relationships (though definitely towards the more informal end of the spectrum).