I have pulled hundreds of new fixtures, most are usually 50' cords, the most common cord length found on most pools here in Phoenix, first i disconnect it at the j-box, then tie some nylon string around the 3 wires at the end of the cord at j-box, then wrap some electrical tape around wire and string, then back at the pool with the light removed from the niche and floating in the pool, i tug and pull at the cord until string end appears, if i am unable to break the cord free to pull it through, i then grab a 2'' piece of PVC pipe from my truck about 5'-10' long (what ever pipe i have already cut on my truck) then i wrap the 5' cord length left on the fixture that allows light to be able to be pulled topside on pool deck for bulb replacement (there should be a few feet of cord wrapped around the light when it is removed from niche) and wrap it around the pipe in such a way that it does not slip, and now have the cord wrapped around the pipe with pipe vertical and the cord centered at the niche and the pipe against the pool wall as i stand on the deck i push on the pipe outward to try and break the cord free, wrapping the pipe around the cord pulls the pipe towards the wall that is used for leverage to break cord free, this provides the additional oomff, and leverage, that just pulling on it while inside the pool doesn't give you, the amount of pressure to break it free can range from a little push to pushing the pipe hard enough to flex the pipe until it gives, once the initial pressure begins to pull the cord out you can get back in the pool and pull it out by hand.
Some cords are tough until you apply enough pressure on them to break cord free, it is just the initial breaking free of the cord that is the hardest part sometimes, then pull the cord through, cut the string from the cord in pool, tie the string to the new light cord, and start pulling the string from the j-box until the cord from new light appears and hook up light. i weave the string around the 3 wires at the end of light cord, and tie it a few times between weaves, then wrap more tape around it, and pull (you want the string to be able to be pulled on without having it slip off off new cord) because i always pull new lights by myself (there is no need for two people) you will have to go back and forth between j-box and pool to unravel cord as it goes into light niche a few times but one person can do this, because i work alone, and it is not practical to drag someone along with me to help change a light, i have learned to do it without help, if you have help that's okay to, one to pull, and one to guide light cord through.
maybe 1 out of 100 light pulls i have done were so hard that i did stretch, and break the cord when trying to pull the light, but it can happen, these were usually on unusual 100' light pulls on some crazy high end home carved out of the side of a mountain or something, it takes quite a bit of effort to break the cord, but usually there's enough cord to re wrap it and try again, or pull it from j-box side etc.
Some lights are going to need that additional leverage to break free when you can't pull it through by pulling on it, don't be afraid to apply more pressure to break it free as i have described, it will work.