I started off this hobby with a 2.5G pico with a HOB filter.
Unless I interpreted wrongly, for your intended shallow pico tank, the only nutrient export is going to be 100% weekly WC. Is that right? Actually, I feel 100% WC is too drastic. Your LS is being subjected to a stressful condition every week because of 100% WC.
Instead of a wavemaker (which in any case would likely cause a storm in a pico), I would suggest to install a small HOB Filter instead. This way, you get some filtration for the water, plus the returning water will provide good water movement. And weekly 20%-40% WC should be sufficient to keep the tank in good condition, unless you tend to overfeed your LS.