Never seen one of the style you are speaking of.
Handy with tools?
Take it apart and clean it, and put it back together.
Make note of how it's assembled when you take it apart, and reverse the order.
They put it together, it can be taken apart, unless the regulator body is "crimped" together, instead of "screwed" together, which I highly doubt.
Start by backing the gas pressure adjustment knob all the way out, until you feel some slight resistance, stop there, then disassemble from there.
Soap and hot water will clean it, just keep your gauges out of the solution.
