Mixing some humour into a Warhammer 40.000 game shouldn't be too difficult. One way would be to simply pop the player character in as a straight-man to all the Warhammer tomfoolery.
Here's an idea. There must be many worlds rather isolated from the Imperium. The weirdo priest people from Terra haven't called for centuries, and all the nasties are far away enough for the place to cultivate a modicum of functionality and pleasantness. The Sensible System, with planets that are actually decent to live on.
The PC could be a member of a noble family in the System Sensibelus, and given the usual officer title the family has bestowed their children of age for years.
Meanwhile, in an office complex that looks like a morbidly obese Notre Dame with syphillis, a miserable clerk in a robe discovers that the Sensible System exist one day while he's dusting the titanic archives and sorting the skull heap. He notify his superiors and eventually, the Imperium arrives to cash in, and Mr. or Ms. PC from the Sensible System is forced to live up to the officer rank and is sent off to the more ridiculous segments of the galaxy to take command and do ridiculous war on preposterous enemies.
Another idea would be to go a similar route as Brazil the film. You are a robed clerk in a stupidly huge administration complex, tasked with openly pointless busywork, handling files about wars no one remembers and planets dead for centuries. That and lighting candles and wheelbarrowing skulls from place to place.
Then, weird things start to happen. You meet a certain someone who gives a bit of colour to your dystopian life. At which point you are declared a heretic, and need to escape through the Gothic-Ridiculous hive city, on a journey that will take you beyond the furthest stars.
-"Why do the Space Marines over there wear those weird parchment loincloths for? Is there some sort of... Exhaust hatch there that they are modest about?"
-"I do not know... But I know that you can tell the important ones apart from the scrubs, though. They're the ones without helmets."
-"Why? I mean, it's like a big, pale potato on top of a coffeeaneus machinare. Who'd miss that?"
-"Well, everyone, it seems. And they hit the marines that do wear helmets instead. Come to think of it, that armour is useless. They just get shot and fall over anyway, don't they?"
-"Maybe they ran out of all the real armour over the years and made them out of cardious bordae instead..."