I don’t think that would help very much - even if the coax is matched well at both ends, there will be some leakage through the braid, rather than “common mode” current flowing along the outside (which could be reduced by coiling etc)
The problem can be minimised by using low loss coax which will have some combination of: close weave braid or double layer of braid or foil as well as braid.
Having said that, I think it is something to be aware of, rather than worry too much about.
On our field day site, I recently set up my SG labs transverter, with a couple of metres of RG58 feeding it from the FT817 at a power level of 0.5 W, to have a dabble on 23cm.
I had a (non scoring) CW contact with our 2m contest station which was about 300 yards away, but the signal level was nothing like enough to cause them a problem - they would have had a quiet word with me if it was
They were running 400W to a pair of 17 ele yagis, but although they were quite loud at my end (!) their signal didn’t cause me any problems either, beyond a few KHz each side.
Strictly back to topic, I mount my transverters (23 and 13) on the back end of the antenna boom, which makes for a nice short feeder, and also helps to balance the antenna against gravity and windage.
This is 23cm, where the transverter is in a waterproof box, which has enough room inside to coil all the cables for transport. They remain connected to the transverter which makes setup / take down a bit quicker.
This is the 13cm setup, not a great photo, but you can just see one of the transverter SMA connectors (for an external reference, unused) poking up at the near end of the boom. The transverter is attached with some thin rubber bungy cord, and the whole assembly is mounted on a camera tripod at a point between the transverter and the Yagi reflector, using a home brew saddle made of wood and paxolin:
(Beaming north from Long Mynd, lights of Shrewsbury in the distance)
Have fun, Tom,