Rather than rely on that tiny airbell, far better to dive a short distance further and do the two sumps as one dive. BUT - if free diving, there's loads of things that can be done to make it safer.
Be warm - full (well maintained) neoprene including hood and gloves.
Correct buoyancy - wear lead weights as necessary. (Don't fight the sump - understand how to glide through effortlessly.)
Be able to see properly, achieved by a combination of bright (multiple) lights and a good mask. Someone holding a light in the water (if possible) at the far end as you dive through will greatly help if underconfident. The better you can see the more easily you'll spot submerged obstacles (such as the roll of rusty fence wire I once encountered in the long Rowten sump, washed in by a flood shortly beforehand).
Be knowledgable - get properly clued up on the layout of the sumps, how recently the lines have been inspected / replaced, know what weather and other factors influence the clarity of the water, etc. Try to understand the passage morphology - so you know what likely direction cross joints run in etc.
Have a kitted diver check the underwater route ahead of your free dive if this is practicable.
In short, treat it as a full on cave dive but without the tanks.
Be bloody careful.
