The schools I applied to have been pretty cool about this (both getting paper letters instead of electronic, and vice versa).
I had one which specified 'online only' but my writers gave me paper letters (sealed and stuff - but because I'm overseas, it was much easier and cheaper for the letters to go in sealed envelopes at the recommenders', then get sent to me to go in with the rest of my materials). The school took these with no problems, just a note that it slows down the process a little as they would need to scan the letters to make them available to other departments.
And right now I'm dealing with a bunch of letters that have been caught up in a mail strike here - should have arrived before Christmas and still aren't here! One of my school's deadlines was Jan 1, and I emailed them a few days ahead to explain the situation and say that the letters were on their way. This particular school was adamant about paper letters ONLY (and, weirdly, required cover sheets on those recommendations only for international students), but sent me back an email while the office was closed saying, "If the letters still haven't arrived by the time the school reopens, your writers can just email their letters in to complete your application".
So, I'm pretty sure that getting letters in a different format is no big drama.