The only reason to use external power with the SX-600 is to light up the meters. This requires 12V. I've had one of these meters for years and very seldom use the power cord. I don't have it installed permanently, however. Maybe it would be nice to lighted if it stayed in my shack.
The Alinco has 12V clips on the front and a cigarette lighter adapter. Yes, its variable from 5-15 volts, but if you are powering radios from it you would be running 12 volts anyway, wouldn't you? I used to have one until it failed.
I'm not sure what the OP is asking since the SWR meter works off the current in the coax and as others has said the + 12 is only for illumination, and you can see the needle move if there is light in the room.
The OP did not say what kind of radio he plans on using it with?
Is it a 50 watt mobile or a handheld?
As long as your power supply provides 12vdc and your meter requires 12vdc for illumination, go ahead and hook it up. As someone mentioned, the meter lights will draw only what they need from the power supply. For safety's sake, however, I would also recommend that you fuse the circuit to protect from a direct short.