So this series was just posted to Amazon the other day after only being a couple of specials for quite a while. Episode 10 is "Something to Squawk About / If You Give a Moose a Cold, though the title display at the beginning reads simply "Sick Day." All of Oliver and Mouse's friends - Moose, Pig, Dog and Cat get a cold and there are sneezes from three out of four of them.
Moose - 11:48, 14:40
Pig - 15:06 (offscreen), 15:23 (double)
Dog - 18:33
Also, beginning 15:49, a scene-changer depicted many boxes of tissues is used, and each time it's accompanied by a high-itched sneeze.
As far as I know, this is only available on Amazon right now, for those either on Prime or Amazon Video.