Overhaul can use his quirk whenever his hands touch the specific thing he wants to disassemble or assemble, including living organism.
In the past, when he recruited Kendo Rappa, a heavily experienced brawler, into the Shie Hassaikai, Kendo proposed that, in order to gain his servitude, Overhaul has to defeat him in battle. But just as Kendo prepared an attack, the Yakuza leader effortlessly disassembled, then reassembled Kendo.
This means that he can reassemble any living organism that he touches back to it's former state, although the series didn't point out if there is a time limit for reassembling "living" things giving that organisms die after a short time.
So I am inclined to believe that he can reassemble living organism in the short span of time that they are "alive". For exemple, if Mr Compress's wound would heal then it could not be reassembled anymore.