Custom Handheld Device from Velleman Components/Modules

I would like to create my own handheld device which logically consists of “Velleman HPG1 Pocket Generator + Velleman HPS140I Pocket Scope”.
The generator will need to send predominantly Sine waveform signals to a wood-mounted piezoelectric transducer.
The scope will then need to collect its signal from a second wood-mounted piezoelectric transducer.
I would like those signals to be Phase-Correct-(D/F)FT-transformed and stored for retrieval along with the time base signals.

On the device, I would still like to show 2 separate physical LCD screens (1 each for the generator and the scope).
I would like the sine signals of each waveform to be captured and time-synchronized (ie. both the generator form and scope-captured data).
Can the generator trigger the scope, for example ?

The stored time and frequency data should be stored and retrievable for processing on the desktop.
Of course, USB transfer is preferable to PC card, but I would also consider an Arduino overlay to add these functions (where I might even be able to transfer over Bluetooth ?)

Lastly, on the topic of Arduino, could such an assembly of Generator + Scope be controlled by your Arduino shield ?

Can you advise me on kits/parts to purchase in order to achieve these things ?