Steering column switch removal

'81 308 GTSi, the inboard end of the headlight stalk has broken off inside the housing, so the plan is to remove the entire column switch assembly and send it off to @Verell.
Picture below shows where I am with the removal so far: Everything taken off and the switch assembly separated from its housing. But the assembly still can't be removed because the wires are threaded through the opening in the housing and the connectors are too big to fit through that opening.
So.... Is there an an easy way to remove that housing, or do I have to remove the wires from the connectors?
(Last time I this had apart I did the wires, I'm looking for an alternative this time around)


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What is involved in unscrewing the housing?