I've never understood the desire to go through the resurgence...
Wade down the river until waist deep (at which point you can see the resurgence ahead). If I remember correctly there's a sign saying don't go any further. Exit the cave via the entrance to your left (daylight obvious if I remember correctly). Follow the path outside the cave, visit the outside of the resurgence and re-enter the cave through one of the other nearby entrances. This is all perfectly safe and at most you miss out on 100 m of wading / swimming in water / pointlessly getting bloody cold.
The other place to be wary is White Horse Pool - as per posts above, jumping in for a swim and getting cold shock has the potential to be dangerous. A lot of years ago a friend of mine thought it would be fun to jump in whilst snow melt was running through the cave (without wearing appropriate clothing for doing so). Once the rest of us had finishing pissing ourselves laughing we eventually helped him out of the water. The muddy bank which is an obvious jumping in point is suddenly 'very slippery' when you're wet and cold. We'd basically finished our trip and 1 of 4 decided to take the swimming route back to the main entrance whilst the other 3 thought the dry option would be better. The net result was 4 took the dry option, but 1 was a bit 'drippy'.
Great cave to bugger about and have fun providing you avoid the resurgence.
Tim