I've had a discussion about this with a composer at BU once and he said there is a high-tech program that basically lays out a spectrum of sound, and with this you can basically edit specific pitches made by specific timbre--i.e. if a violin is playing a wrong note at a certain time, you can edit it to a correct note. With this, editing out coughs or sniffs should be easy. Problem is, I don't know the name of the program (I know that it exists because the composer I talked to saw this in person), and it's supposed to be extremely expensive.
This is a possibility, albeit a remote one, although my guess is that Pärt, if his symphony is popular enough to be recorded again, or if he and an orchestra are to sign a deal to perform it, will release another recording. I mean, his 4th is pretty recent, so I'd expect future recordings...