Hello, I'm TV Tech1 and I'll be working with you to identify and help you resolve your problem.
I would assume the speaker cut out is done by the headphone jack itself. It would have a mechanical switch on it that disconnects the speakers.
Your switch is similar to this design which basically disconnects the speakers when the headphone jack is inserted --
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The real problem is finding a switch that has a long enough threaded neck to replace the old headphone jack. you don't want a short neck (or socket) that won't allow you to place the nut on the bracket mount and tighten it down.
And Philips doesn't seem to supply that specific part. It may be because it's a universal fit found at major component suppliers.