Most important that you check that you are insured to work near/over/in water with your insurance company best done before works start and documented on your certificate. They may ask for what control methods /competence and how much work/time you will spend in/over or near water.
At least have an e mail that documents this confirmation.
If your going to be doing a bit of this work and your employed you may suggest that someone is sent to complete some training rather than relying on what others suggest or whats on the net.
It now gets a bit murky, a bit like arb crane courses as HSE don't formally have an ACOP for working as we would do in water, the closest at the low end is safety near water & fitting basic PPE HSE - Publications: Free Leaflets - Working near water
There's plenty on legionella disease mind....
It then go's to the extremes of working in confined spaces (Sewers etc) and commercial diving both of little relevance so there's nothing to guide us with best practice.
So when I put blokes in or near the water they have all attended either the Swiftwater Rescue Technican course Swiftwater and Flood Rescue Technician (SRT)
This is a 4 day course that you may deem as costly/extreme but that person will be able to give you a good insight into the measures/PPE you will require , the associated risks that you may encounter with the site (Flash floods/weirs/tidal pollution decontamination etc)and assist in completing your RAM's for client.
OR have attended a ROSPA type one day water awareness course designed for persons that may be in vicinity to water and have to carry out a rescue (Canal lock keeper/Police etc)
Water Safety - RoSPA
A 1 day course that is 90% land based and includes fitting some basic PPE and carrying out bank based rescues using non specialist equipment.
Also as pointed out there are many items of PPE that are available some suited to different scenarios if your doing lots of water work its good to have an array of PFD's/self inflating devices /drysuits/throwlines maybe even a boat or floating works platform and a good working knowledge about ropes/knots or No knots/harness's and being tied into a system when in water which could be more dangerous than not being tied in.
Chainsaw trousers can go under drysuits with no issues but chainsaw boots for protection v Canyon Boots for stability and grip is a debate I leave for the individual to decide.
A wading stick or 2 fibre polesaw sections with a hook on the top (They float)
A good toolbox talk just like crane work with any other agencies and comms for all (Radio headsets ideal)
One worker in the water with someone close (On bank or in water) watching there back and passing saws/tools/wading stick etc and then someone equipped/prepared to carry out a rescue down stream from works who is not involved in the works (This can make this nature of works costly for a client but it is essential to ensure safety of workers)
I do understand that many will deem the above as an extreme will giggle & nod there head don wellies and speedo's and just get in there as its like a paddling pool whatever you choose stay safe & look after your staff.