Water-based exercise has many potential advantages over land-based exercise programs. The warmth and buoyancy combined with elimination of gravity eases joint pain and improves range-of-motion. And because the water gives resistance to movement, you can vary how much or how little resistance there is by standing in shallow versus deeper water and/or by moving slower or faster through the water.
But giving up core training for an aquatic program may not be the best approach. Both have specific advantages and accomplish different things. Core training is especially important for anyone with spinal instability. Strengthening the abdominal and trunk muscles helps provide support and stiffness for a spine that is too loose or lax.
You may be able to reproduce core training in the water but it’s best to have an expert help get you started. Physical therapists offer aquatic therapy for patients with all kinds of problems, not just low back pain. Another advantage of aquatic-based exercise is that it can give you the aerobic component that’s not possible on land if your spine isn’t strong enough or stable enough for that type of exercise.
Would it be possible to do a little cross-training? Perhaps you could alternate days and still get in 3 to 4 days of each type of exercise over a week’s time. In any case, don’t just stop doing one set of exercises and launch into a different type. Give your body a chance to respond and react to the new program. Monitor your symptoms. If they get worse, slowly reintroduce the core exercises you’ve been doing. If you get better, then perhaps you were on to something that works well for you!