For what it's worth, here's what Berlioz has to say in his Treatise on Instrumentation:
The composer, when indicating the use of mutes in the middle of a piece (by the words con sordini), must not forget to allow sufficient time for putting them on. He should provide a rest in the violins, equal in length to about two bars in 4-4 time, moderato. The testrest may be shorter when the words senza sordini indicate that the mutes are to be removed; this can be done in much less time.
If you do need a transition to or from mutes during continuous playing, you could perhaps divide a section and have half the players start playing with mutes at the same time that the other half end an unmuted phrase.