You could use a short length of a thinner, more flexible coax, connected to your coax lead-in.
In my case, my 396T sits on a partially opened desk drawer. I have 2 homebrew antennas with leads, nearby. The coax in use is 'clamped' by an adjacent drawer, so it doesn't move and cause any problems.
Since the coax leads are terminated with an F connector, I use the F to SMA adapter, so I can quick change leads without adding any strain.
In your case, I would try to strategically place a few of these:
If you are using an antenna connected with coax try placing two 90 degree connectors onto it so the cable will be parallel to the case of the radio. This is what I do in my car and it has worked perfectly for years.
get some shrink tubing,and some strong string,
I use round shoelace.
youll need to loop it,slide shrinktube over it,
leave about 2 inches on the loop end,1 inch on the open end,
slide another piece of shrinktube over the loose ends.