Re-wiring my PAS3

I am looking for recommendations as to what I should use to re-wire my modified Dynaco PAS3 Preamp. The stack wiring is simple 22ga. stranded wire with no shield. Ground wires are twisted around the signal wires to provide shielding. I want to replace this with coaxial wire, this should improve shielding. Because of the number of wire runs and the limited space available I will need the coax to be rather thin and flexible. After some research I had landed on two possibilities, RG188 and RG316.These seem to be very similar in most respects the RG316 is just a little smaller in diameter but there is no difference in the gauge.

Is there any reason not to use either of these two cables? And is there any other wire I should consider?

Thanks,
Brent

In my experience, in a good-running PAS with good lead dress, replacement of the twisted pairs with shielded cable makes no difference and may degrade phono performance due to higher capacitance loading on moving magnet cartridges. In my upgraded PAS have had better results in reducing stray hum, even though it was really low already, with a steel shield cut and bent to fit around the (much upgraded) power supply section. I also moved the power transformer to a new home on the outside of the case.