Thanks for your question Sbiriguda.
So the conditions you have defined are:
1. The pouch/sheath must be attached via cord/string.
2. The cord must be fed through both holes of the BCD jacket.
We can easily see the 2 eyelet holes in the BCD but, what is not so easy to observe is where/how the cord would be fed through the pouch/sheath of the line cutter.
Its easy to visualize the cord feeding through the 2 holes in the BCD but, its not as easy to visualize exactly where the cord would be attached to the pouch/sheath.
All I can assume is that it is possible to create a 'loop' of cord (ie a circle).
This means an 'end-to-end' joining knot is needed.
Two end-to-end joining knots spring to mind:
1. #1415 Double fishermans bend; or
2. Zeppelin bend.
A Zeppelin bend is quite secure and can be easily adjusted. It can also be untied if you ever need to remove the cord for any reason.
A double fishermans - once cinched tight, is very difficult to untie (but it is also
very secure).
Links:[ ]
https://www.animatedknots.com/doublefishermans/ [ ]
https://www.animatedknots.com/zeppelin/