I put a low pressure swivel on my GF's inflator hose from the Edge EXP 1st stage she is using. It routes the hose so nice and clean over the shoulder. No need for one on the second stages.
If the OP is using a CDX5 or DX4 first stage I can see putting a swivel on the 1st stage for the octo. Routes it down nice and clean. With it though the 36 is just barely long enough. I'd get rid of the 36 and replace with a 40 on the octo. The CDX and DX first stage LP ports that the octo is often routed from point straight out and create a bit of a loop. Using the swivel here eliminates that.
If the OP is using a CDX5 or DX4 first stage I can see putting a swivel on the 1st stage for the octo. Routes it down nice and clean. With it though the 36 is just barely long enough. I'd get rid of the 36 and replace with a 40 on the octo. The CDX and DX first stage LP ports that the octo is often routed from point straight out and create a bit of a loop. Using the swivel here eliminates that.