Did some research....it was not DangerMouse who had the sneezing fits...and the hamster sidekick was named PenFold
The character Agent 57 had sneezing fits in one episode...
Agent 57: Initially, a master of disguise, Agent 57 later gained the ability to alter his own molecular structure to transform into any appearance he wished. This ability went temporarily out of control in one episode when he contracted a cold, causing him to involuntarily change shape whenever he sneezed. ramming his tea-trolley into a sensitive piece of equipment.
Season 6 Episode 119 "The Spy Who Stayed in with a Cold" "Agent 57" had sneezing fits, Danger Mouse asked him if he could transform himself into his original appearance; Agent 57 obliged, and Danger Mouse looked down at the floorboard of the Mark III and was horrified by the sight (unseen by the audience). After gathering himself from the shock, Danger Mouse asked Agent 57 to please transform into something heavier; Agent 57 transformed into a hippo, and the excess weight dropped the Mark III.
List of Danger Mouse episodes - Wikipedia, the free encyclopedia