Riverknife
On all courses you should bring a small river knife with you if you have one. Anybody working or playing around water with ropes should always have a back-up method of releasing a line under tension.
Some people favor the ease of use and "Rambo-ness" of the sheath / divers knife strapped to some part of their lifejacket or body. Others prefer the subtle looks of the folding knife which can be opened one handed and placed in a suitable positioned pocket in your lifejacket.
Which ever knife you choose the matter of retention should be given careful thought. Do you want to be swimming in a hole with that razor sharp knife on a 1m length of cord whizzing round by your head? Fastex buckles can be used to keep the cord super short when you secure your knife to your jacket. At the same time you can still easily release the knife when needed.