yeap! Without knowing that home store I can definitely say YES.
No shop refuses to sell fireworks. Not even do all home stores sell them but much more shops.
To the ply: check the 2mm ply. I have tried the 1mm and 1.5mm ply also, but the 2mm is much more stable to cut when it comes to fine details.
You can stack cut up to 8 layers of that 2mm ply (blade #3)