From the looks of it, your physiological ability is more than ready. If you're doing 115m dynamic, 40m should be more or less trivial physically.
The 2 things that I see as a challenge are equalization and overall experience - and both are interconnected (and translated to relaxation and confidence in the water). I'd say make use of your pool time. Do a lot of dynamic training and equalization training. That is, trying to make equalization as hard as you can for your self in the pool and then learning to deal with it. Basically trying to reach the bottom of the pool with less and less air - eventually totally empty once you master it. But take it gradually and make absolutely sure you have a partner watching you on the e-dives.
For the experience part - well, one month of training should be plenty. Just try to make sure you don't get carried away and miss most of that due to injury or such - meaning give your self some slack during that month too. Enjoy the diving, get proper rest and don't push too hard. Especially mind your ears and sinuses. If they hurt, stop diving and come back the next day...In other words, be wise about it
Hardest effort doesn't always yield best results - you have to be sort of cunning about it sometimes - know when to back off and recover for a better attempt. This is true for any sport, but especially true in freediving where the possibility of injury is high (eg. ears)
Anyway - in the end, there's no replacement for actual experience in the deep diving, but a good substitute in the pool is simulation dives. They don't do much physiologically, but mentally they're great to boost your confidence and develop routine.
Basically I would see a 40m constant weight dive as:
-Duckdive
-Swim to -10m "efficiently"
-Swim another 10-15m "relaxed"
-Free fall to bottom
-Swim "efficiently" 20 meters
-Swim relaxed 10 meters
-Free float to surface.
This would take about 40 sec to bottom, 40 sec up.
So what you might do is:
-Start with a duckdive, then about 6 kicks pretty hard and 6 really relaxed.
-Then do a short static until clock shows about 40 sec.
-Swim on a good pace for another 35 seconds.
-Come up slowly and as relaxed as possible
-Grab a firm hold of something (simulating grabbing the rope firmly once you're up)
-The point is the dive should end at the same spot it started (like cw) - you cannot come up "in between"
So what would a pool session look like?
-Stretch and warm up
-Dynamic training - for example 3-5 times 80%
-couple of simulated cw dives
-Equalization drills and playing with e-dives
Alternate dynamic with technique drills every other time
On dry land:
-Dry statics
-Stretching and diaphragm stretching
-Visualization (going through the dive in your head again and again in positive manner)
After all this I will back up a little and also say - to me it looks like you're pretty much ready. All you need is to do it and 1 month is plenty of time. Don't stress too much about training. Just go there, have fun and do it. Try to focus on building up confidence and experience with your lead up training. The opposite is less likely to bring results (stress and obsess about it, possibly injure your self and in worst case make the whole attempt impossible). The one technical/physilogical question mark is equalization - with our experience I'm guessing that'll be fine, but it's also possible to learn all you need about equalization at pool depths...So why not do that while you're locked to pool training
