Is it rude to sign off mails with a shorthand This may seem a bit mundane or silly to many but I figured it might be useful for others besides me, hence the question.

My boss (postdoc mentor) is a very kind person, who pretty much exclusively writes in grammatically correct, well articulated sentences and ALWAYS have a nice but relatively formal greeting at the end of the mail. No matter how many times we mail each other in a given day. Even though we are not formal at all when we talk to each other. 

As per usual in Scandinavia, we have a very flat hierarchy here, so everyone (from project students to professors and indeed the dean) is on a first name basis with each other, and there are little formalities that may be commonplace elsewhere. 

We have been working very closely on this project, with almost daily meetings and near 10-15 mails exchanged throughout the day. My previous experience has always been so that once the formalities have been observed, the communication defaults to shorter, more direct mails. 

Given the high-paced exchange between us, I was wondering if it would be rude to write shorter mails that are straight to the point. Specifically I often find myself signing off a mail with a shorthand greeting, e.g. "mvh" instead of "(med) vänliga hälsningar" (which is significantly more formal) or just by writing my name. [The Swedish expressions roughly correspond to "BR" - "Best Regards", respectively].

I thought of asking him if he prefers a more formal tone in our written communication but I don't wanna come across as a pedantic person. Suggestions?
(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).