Let me be a little bit more elaborate on this - I assume you do have legitimate medical reason and are not one of these with tinfoil hats. I was not going to take political route, but to raise awareness of situation here.

Unless you clarify your situation in advance with Singapore ICA (immigrations and customs authority) and have some written letter/message from them so you can present it when you arrive at Changi, if you try to refuse going thru scanner at the gate you obviously won't get to flight and it will immediately raise suspicion. And then, depending how paranoid local personnel is, especially in the light that everywhere in the city are now posters 'what to do during terrorist attack' - they might want to further question you.

So you have an option either to get sorted everything beforehand or depart Singapore via other means - land, boat where these machines are not deployed. What I wanted to say that I would not recommend doing nothing in advance and then refuse going thru scanner at the gate.