Interestingly, you might just have indeed hit the nail on the head. It might be a photoshop after all.
I tried googling "Chee Soon Juan loudhailer", "Did Chee Soon Juan use a loudhailer", etc. and the only hits were some people claiming the ST did some editing to juxtapose Chee with a loudhailer with Goh (but no credible sources). I tried searching google image - but turned up no visuals of Dr Chee with a loudspeaker in hand.
The truth - is unknown to me. Maybe someone who knows can clarify.
But knowing the media's propensity to smear Dr Chee, it's probably not real that he used a loudhailer to shout and chase after Goh Chok Tong. And the amazing thing is - in citizens' minds - he did! That's the power of our MSM smearing. What else can I say...